diff --git a/src/uint/mod.rs b/src/uint/mod.rs
index 26598675..11c5efac 100644
--- a/src/uint/mod.rs
+++ b/src/uint/mod.rs
@@ -12,6 +12,8 @@ mod convert;
 mod eq;
 mod not;
 mod or;
+mod shl;
+mod shr;
 mod rotate;
 mod select;
 mod xor;
@@ -81,7 +83,7 @@ impl<const N: usize, T: PrimUInt, F: Field> UInt<N, T, F> {
 
         for i in 0..N {
             bits[i] = Boolean::constant((bit_values & T::one()) == T::one());
-            bit_values = bit_values >> 1;
+            bit_values = bit_values >> 1u8;
         }
 
         Self {
diff --git a/src/uint/prim_uint.rs b/src/uint/prim_uint.rs
index 963db0f7..7f8c21ca 100644
--- a/src/uint/prim_uint.rs
+++ b/src/uint/prim_uint.rs
@@ -1,3 +1,6 @@
+use core::usize;
+use core::ops::{Shl, ShlAssign, Shr, ShrAssign};
+
 #[doc(hidden)]
 // Adapted from <https://github.com/rust-num/num-traits/pull/224>
 pub trait PrimUInt:
@@ -5,6 +8,32 @@ pub trait PrimUInt:
     + num_traits::PrimInt
     + num_traits::WrappingAdd
     + num_traits::SaturatingAdd
+    + Shl<usize, Output = Self>
+    + Shl<u8, Output = Self>
+    + Shl<u16, Output = Self>
+    + Shl<u32, Output = Self>
+    + Shl<u64, Output = Self>
+    + Shl<u128, Output = Self>
+    + Shr<usize, Output = Self>
+    + Shr<u8, Output = Self>
+    + Shr<u16, Output = Self>
+    + Shr<u32, Output = Self>
+    + Shr<u64, Output = Self>
+    + Shr<u128, Output = Self>
+    + ShlAssign<usize>
+    + ShlAssign<u8>
+    + ShlAssign<u16>
+    + ShlAssign<u32>
+    + ShlAssign<u64>
+    + ShlAssign<u128>
+    + ShrAssign<usize>
+    + ShrAssign<u8>
+    + ShrAssign<u16>
+    + ShrAssign<u32>
+    + ShrAssign<u64>
+    + ShrAssign<u128>
+    + Into<u128>
+    + _private::Sealed
     + ark_std::UniformRand
 {
     type Bytes: NumBytes;
@@ -134,3 +163,14 @@ pub trait NumBytes:
 
 #[doc(hidden)]
 impl<const N: usize> NumBytes for [u8; N] {}
+
+
+mod _private {
+    pub trait Sealed {}
+
+    impl Sealed for u8 {}
+    impl Sealed for u16 {}
+    impl Sealed for u32 {}
+    impl Sealed for u64 {}
+    impl Sealed for u128 {}
+}
\ No newline at end of file
diff --git a/src/uint/shl.rs b/src/uint/shl.rs
new file mode 100644
index 00000000..2aaf474c
--- /dev/null
+++ b/src/uint/shl.rs
@@ -0,0 +1,160 @@
+use ark_ff::PrimeField;
+use ark_relations::r1cs::SynthesisError;
+use ark_std::{ops::Shl, ops::ShlAssign};
+
+use crate::boolean::Boolean;
+
+use super::{PrimUInt, UInt};
+
+impl<const N: usize, T: PrimUInt, F: PrimeField> UInt<N, T, F> {
+    fn _shl_u128(&self, other: u128) -> Result<Self, SynthesisError> {
+        if other < N as u128 {
+            let mut bits = [Boolean::FALSE; N];
+            for (a, b) in bits[other as usize..].iter_mut().zip(&self.bits) {
+                *a = b.clone();
+            }
+            
+            let value = self.value.and_then(|a| Some(a << other));
+            Ok(Self {
+                bits,
+                value,
+            })
+        } else {
+            panic!("attempt to shift left with overflow")
+        }
+    }
+}
+
+impl<const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> Shl<T2> for UInt<N, T, F> {
+    type Output = Self;
+
+    /// Output `self << other`.
+    ///
+    /// If at least one of `self` and `other` are constants, then this method
+    /// *does not* create any constraints or variables.
+    ///
+    /// ```
+    /// # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+    /// // We'll use the BLS12-381 scalar field for our constraints.
+    /// use ark_test_curves::bls12_381::Fr;
+    /// use ark_relations::r1cs::*;
+    /// use ark_r1cs_std::prelude::*;
+    ///
+    /// let cs = ConstraintSystem::<Fr>::new_ref();
+    /// let a = UInt8::new_witness(cs.clone(), || Ok(16))?;
+    /// let b = 1;
+    /// let c = UInt8::new_witness(cs.clone(), || Ok(16 << 1))?;
+    ///
+    /// (a << 1).enforce_equal(&c)?;
+    /// assert!(cs.is_satisfied().unwrap());
+    /// # Ok(())
+    /// # }
+    /// ```
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shl(self, other: T2) -> Self::Output {
+        self._shl_u128(other.into()).unwrap()
+    }
+}
+
+impl<'a, const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> Shl<T2> for &'a UInt<N, T, F> {
+    type Output = UInt<N, T, F>;
+
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shl(self, other: T2) -> Self::Output {
+        self._shl_u128(other.into()).unwrap()
+    }
+}
+
+impl<const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> ShlAssign<T2> for UInt<N, T, F> {
+    /// Sets `self = self << other`.
+    ///
+    /// If at least one of `self` and `other` are constants, then this method
+    /// *does not* create any constraints or variables.
+    ///
+    /// ```
+    /// # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+    /// // We'll use the BLS12-381 scalar field for our constraints.
+    /// use ark_test_curves::bls12_381::Fr;
+    /// use ark_relations::r1cs::*;
+    /// use ark_r1cs_std::prelude::*;
+    ///
+    /// let cs = ConstraintSystem::<Fr>::new_ref();
+    /// let mut a = UInt8::new_witness(cs.clone(), || Ok(16))?;
+    /// let b = 1;
+    /// let c = UInt8::new_witness(cs.clone(), || Ok(16 << 1))?;
+    ///
+    /// a <<= b;
+    /// a.enforce_equal(&c)?;
+    /// assert!(cs.is_satisfied().unwrap());
+    /// # Ok(())
+    /// # }
+    /// ```
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shl_assign(&mut self, other: T2) {
+        let result = self._shl_u128(other.into()).unwrap();
+        *self = result;
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{
+        alloc::{AllocVar, AllocationMode},
+        prelude::EqGadget,
+        uint::test_utils::{run_binary_exhaustive_with_native, run_binary_random_with_native},
+        R1CSVar,
+    };
+    use ark_ff::PrimeField;
+    use ark_test_curves::bls12_381::Fr;
+
+    fn uint_shl<T: PrimUInt, const N: usize, F: PrimeField>(
+        a: UInt<N, T, F>,
+        b: T,
+    ) -> Result<(), SynthesisError> {
+        let cs = a.cs();
+        let b = b.into() % (N as u128);
+        let computed = &a << b;
+        let expected_mode = if a.is_constant() {
+            AllocationMode::Constant
+        } else {
+            AllocationMode::Witness
+        };
+        let expected = UInt::<N, T, F>::new_variable(
+            cs.clone(),
+            || Ok(a.value()? << b),
+            expected_mode,
+        )?;
+        assert_eq!(expected.value(), computed.value());
+        expected.enforce_equal(&computed)?;
+        if !a.is_constant() {
+            assert!(cs.is_satisfied().unwrap());
+        }
+        Ok(())
+    }
+
+    #[test]
+    fn u8_shl() {
+        run_binary_exhaustive_with_native(uint_shl::<u8, 8, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u16_shl() {
+        run_binary_random_with_native::<1000, 16, _, _>(uint_shl::<u16, 16, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u32_shl() {
+        run_binary_random_with_native::<1000, 32, _, _>(uint_shl::<u32, 32, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u64_shl() {
+        run_binary_random_with_native::<1000, 64, _, _>(uint_shl::<u64, 64, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u128_shl() {
+        run_binary_random_with_native::<1000, 128, _, _>(uint_shl::<u128, 128, Fr>).unwrap()
+    }
+}
diff --git a/src/uint/shr.rs b/src/uint/shr.rs
new file mode 100644
index 00000000..dbcdc8d7
--- /dev/null
+++ b/src/uint/shr.rs
@@ -0,0 +1,160 @@
+use ark_ff::PrimeField;
+use ark_relations::r1cs::SynthesisError;
+use ark_std::{ops::Shr, ops::ShrAssign};
+
+use crate::boolean::Boolean;
+
+use super::{PrimUInt, UInt};
+
+impl<const N: usize, T: PrimUInt, F: PrimeField> UInt<N, T, F> {
+    fn _shr_u128(&self, other: u128) -> Result<Self, SynthesisError> {
+        if other < N as u128 {
+            let mut bits = [Boolean::FALSE; N];
+            for (a, b) in bits.iter_mut().zip(&self.bits[other as usize..]) {
+                *a = b.clone();
+            }
+            
+            let value = self.value.and_then(|a| Some(a >> other));
+            Ok(Self {
+                bits,
+                value,
+            })
+        } else {
+            panic!("attempt to shift right with overflow")
+        }
+    }
+}
+
+impl<const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> Shr<T2> for UInt<N, T, F> {
+    type Output = Self;
+
+    /// Output `self >> other`.
+    ///
+    /// If at least one of `self` and `other` are constants, then this method
+    /// *does not* create any constraints or variables.
+    ///
+    /// ```
+    /// # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+    /// // We'll use the BLS12-381 scalar field for our constraints.
+    /// use ark_test_curves::bls12_381::Fr;
+    /// use ark_relations::r1cs::*;
+    /// use ark_r1cs_std::prelude::*;
+    ///
+    /// let cs = ConstraintSystem::<Fr>::new_ref();
+    /// let a = UInt8::new_witness(cs.clone(), || Ok(16))?;
+    /// let b = 1;
+    /// let c = UInt8::new_witness(cs.clone(), || Ok(16 >> 1))?;
+    ///
+    /// (a >> 1).enforce_equal(&c)?;
+    /// assert!(cs.is_satisfied().unwrap());
+    /// # Ok(())
+    /// # }
+    /// ```
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shr(self, other: T2) -> Self::Output {
+        self._shr_u128(other.into()).unwrap()
+    }
+}
+
+impl<'a, const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> Shr<T2> for &'a UInt<N, T, F> {
+    type Output = UInt<N, T, F>;
+
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shr(self, other: T2) -> Self::Output {
+        self._shr_u128(other.into()).unwrap()
+    }
+}
+
+impl<const N: usize, T: PrimUInt, F: PrimeField, T2: PrimUInt> ShrAssign<T2> for UInt<N, T, F> {
+    /// Sets `self = self >> other`.
+    ///
+    /// If at least one of `self` and `other` are constants, then this method
+    /// *does not* create any constraints or variables.
+    ///
+    /// ```
+    /// # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+    /// // We'll use the BLS12-381 scalar field for our constraints.
+    /// use ark_test_curves::bls12_381::Fr;
+    /// use ark_relations::r1cs::*;
+    /// use ark_r1cs_std::prelude::*;
+    ///
+    /// let cs = ConstraintSystem::<Fr>::new_ref();
+    /// let mut a = UInt8::new_witness(cs.clone(), || Ok(16))?;
+    /// let b = 1;
+    /// let c = UInt8::new_witness(cs.clone(), || Ok(16 >> 1))?;
+    ///
+    /// a >> b;
+    /// a.enforce_equal(&c)?;
+    /// assert!(cs.is_satisfied().unwrap());
+    /// # Ok(())
+    /// # }
+    /// ```
+    #[tracing::instrument(target = "r1cs", skip(self, other))]
+    fn shr_assign(&mut self, other: T2) {
+        let result = self._shr_u128(other.into()).unwrap();
+        *self = result;
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{
+        alloc::{AllocVar, AllocationMode},
+        prelude::EqGadget,
+        uint::test_utils::{run_binary_exhaustive_with_native, run_binary_random_with_native},
+        R1CSVar,
+    };
+    use ark_ff::PrimeField;
+    use ark_test_curves::bls12_381::Fr;
+
+    fn uint_shr<T: PrimUInt, const N: usize, F: PrimeField>(
+        a: UInt<N, T, F>,
+        b: T,
+    ) -> Result<(), SynthesisError> {
+        let cs = a.cs();
+        let b = b.into() % (N as u128);
+        let computed = &a >> b;
+        let expected_mode = if a.is_constant() {
+            AllocationMode::Constant
+        } else {
+            AllocationMode::Witness
+        };
+        let expected = UInt::<N, T, F>::new_variable(
+            cs.clone(),
+            || Ok(a.value()? >> b),
+            expected_mode,
+        )?;
+        assert_eq!(expected.value(), computed.value());
+        expected.enforce_equal(&computed)?;
+        if !a.is_constant() {
+            assert!(cs.is_satisfied().unwrap());
+        }
+        Ok(())
+    }
+
+    #[test]
+    fn u8_shr() {
+        run_binary_exhaustive_with_native(uint_shr::<u8, 8, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u16_shr() {
+        run_binary_random_with_native::<1000, 16, _, _>(uint_shr::<u16, 16, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u32_shr() {
+        run_binary_random_with_native::<1000, 32, _, _>(uint_shr::<u32, 32, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u64_shr() {
+        run_binary_random_with_native::<1000, 64, _, _>(uint_shr::<u64, 64, Fr>).unwrap()
+    }
+
+    #[test]
+    fn u128_shr() {
+        run_binary_random_with_native::<1000, 128, _, _>(uint_shr::<u128, 128, Fr>).unwrap()
+    }
+}
diff --git a/src/uint/test_utils.rs b/src/uint/test_utils.rs
index 13716833..5b3503e8 100644
--- a/src/uint/test_utils.rs
+++ b/src/uint/test_utils.rs
@@ -28,6 +28,17 @@ pub(crate) fn test_binary_op<T: PrimUInt, const N: usize, F: PrimeField>(
     test(a, b)
 }
 
+pub(crate) fn test_binary_op_with_native<T: PrimUInt, const N: usize, F: PrimeField>(
+    a: T,
+    b: T,
+    mode_a: AllocationMode,
+    test: impl FnOnce(UInt<N, T, F>, T) -> Result<(), SynthesisError>,
+) -> Result<(), SynthesisError> {
+    let cs = ConstraintSystem::<F>::new_ref();
+    let a = UInt::<N, T, F>::new_variable(cs.clone(), || Ok(a), mode_a)?;
+    test(a, b)
+}
+
 pub(crate) fn run_binary_random<const ITERATIONS: usize, const N: usize, T, F>(
     test: impl Fn(UInt<N, T, F>, UInt<N, T, F>) -> Result<(), SynthesisError> + Copy,
 ) -> Result<(), SynthesisError>
@@ -65,6 +76,43 @@ where
     Ok(())
 }
 
+pub(crate) fn run_binary_random_with_native<const ITERATIONS: usize, const N: usize, T, F>(
+    test: impl Fn(UInt<N, T, F>, T) -> Result<(), SynthesisError> + Copy,
+) -> Result<(), SynthesisError>
+where
+    T: PrimUInt,
+    F: PrimeField,
+{
+    let mut rng = ark_std::test_rng();
+
+    for _ in 0..ITERATIONS {
+        for mode_a in modes() {
+            let a = T::rand(&mut rng);
+            let b = T::rand(&mut rng);
+            test_binary_op_with_native(a, b, mode_a, test)?;
+        }
+    }
+    Ok(())
+}
+
+pub(crate) fn run_binary_exhaustive_with_native<const N: usize, T, F>(
+    test: impl Fn(UInt<N, T, F>, T) -> Result<(), SynthesisError> + Copy,
+) -> Result<(), SynthesisError>
+where
+    T: PrimUInt,
+    F: PrimeField,
+    RangeInclusive<T>: Iterator<Item = T>,
+{
+    for (mode_a, a) in test_utils::combination(T::min_value()..=T::max_value()) {
+        for b in T::min_value()..=T::max_value() {
+            test_binary_op_with_native(a, b, mode_a, test)?;
+        }
+    }
+    Ok(())
+}
+
+
+
 pub(crate) fn run_unary_random<const ITERATIONS: usize, const N: usize, T, F>(
     test: impl Fn(UInt<N, T, F>) -> Result<(), SynthesisError> + Copy,
 ) -> Result<(), SynthesisError>