diff --git a/zokrates_analysis/src/zir_propagation.rs b/zokrates_analysis/src/zir_propagation.rs
index 8582b33b..1a026b17 100644
--- a/zokrates_analysis/src/zir_propagation.rs
+++ b/zokrates_analysis/src/zir_propagation.rs
@@ -1,6 +1,8 @@
+use num::traits::Pow;
+use num_bigint::BigUint;
 use std::collections::HashMap;
 use std::fmt;
-use std::ops::{BitAnd, BitOr, BitXor, Shl, Shr};
+use std::ops::{BitAnd, BitOr, BitXor, Mul, Shr, Sub};
 use zokrates_ast::zir::types::UBitwidth;
 use zokrates_ast::zir::{
     result_folder::*, Conditional, ConditionalExpression, ConditionalOrExpression, Expr, Id,
@@ -312,15 +314,30 @@ impl<'ast, T: Field> ResultFolder<'ast, T> for ZirPropagator<'ast, T> {
                             ..
                         },
                     ) if by == 0 => Ok(e),
+                    (
+                        _,
+                        UExpression {
+                            inner: UExpressionInner::Value(by),
+                            ..
+                        },
+                    ) if by as usize >= T::get_required_bits() => {
+                        Ok(FieldElementExpression::Number(T::from(0)))
+                    }
                     (
                         FieldElementExpression::Number(n),
                         UExpression {
                             inner: UExpressionInner::Value(by),
                             ..
                         },
-                    ) => Ok(FieldElementExpression::Number(
-                        T::try_from(n.to_biguint().shl(by as usize)).unwrap(),
-                    )),
+                    ) => {
+                        let two = BigUint::from(2usize);
+                        let mask: BigUint = two.pow(T::get_required_bits()).sub(1usize);
+
+                        Ok(FieldElementExpression::Number(
+                            T::try_from(n.to_biguint().mul(two.pow(by as usize)).bitand(mask))
+                                .unwrap(),
+                        ))
+                    }
                     (e, by) => Ok(FieldElementExpression::LeftShift(box e, box by)),
                 }
             }
@@ -335,6 +352,15 @@ impl<'ast, T: Field> ResultFolder<'ast, T> for ZirPropagator<'ast, T> {
                             ..
                         },
                     ) if by == 0 => Ok(e),
+                    (
+                        _,
+                        UExpression {
+                            inner: UExpressionInner::Value(by),
+                            ..
+                        },
+                    ) if by as usize >= T::get_required_bits() => {
+                        Ok(FieldElementExpression::Number(T::from(0)))
+                    }
                     (
                         FieldElementExpression::Number(n),
                         UExpression {
@@ -948,6 +974,115 @@ mod tests {
             );
         }
 
+        #[test]
+        fn left_shift() {
+            let mut propagator = ZirPropagator::<Bn128Field>::default();
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::LeftShift(
+                    box FieldElementExpression::identifier("a".into()),
+                    box UExpressionInner::Value(0).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::identifier("a".into()))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::LeftShift(
+                    box FieldElementExpression::Number(Bn128Field::from(2)),
+                    box UExpressionInner::Value(2 as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(8)))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::LeftShift(
+                    box FieldElementExpression::Number(Bn128Field::from(1)),
+                    box UExpressionInner::Value((Bn128Field::get_required_bits() - 1) as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::try_from_dec_str("14474011154664524427946373126085988481658748083205070504932198000989141204992").unwrap()))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::LeftShift(
+                    box FieldElementExpression::Number(Bn128Field::from(3)),
+                    box UExpressionInner::Value((Bn128Field::get_required_bits() - 3) as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::try_from_dec_str("10855508365998393320959779844564491361244061062403802878699148500741855903744").unwrap()))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::LeftShift(
+                    box FieldElementExpression::Number(Bn128Field::from(1)),
+                    box UExpressionInner::Value((Bn128Field::get_required_bits()) as u128)
+                        .annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(0)))
+            );
+        }
+
+        #[test]
+        fn right_shift() {
+            let mut propagator = ZirPropagator::<Bn128Field>::default();
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::identifier("a".into()),
+                    box UExpressionInner::Value(0).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::identifier("a".into()))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::identifier("a".into()),
+                    box UExpressionInner::Value(Bn128Field::get_required_bits() as u128)
+                        .annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(0)))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::Number(Bn128Field::from(3)),
+                    box UExpressionInner::Value(1 as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(1)))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::Number(Bn128Field::from(2)),
+                    box UExpressionInner::Value(2 as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(0)))
+            );
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::Number(Bn128Field::from(2)),
+                    box UExpressionInner::Value(4 as u128).annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(0)))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::Number(Bn128Field::max_value()),
+                    box UExpressionInner::Value((Bn128Field::get_required_bits() - 1) as u128)
+                        .annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(1)))
+            );
+
+            assert_eq!(
+                propagator.fold_field_expression(FieldElementExpression::RightShift(
+                    box FieldElementExpression::Number(Bn128Field::max_value()),
+                    box UExpressionInner::Value(Bn128Field::get_required_bits() as u128)
+                        .annotate(UBitwidth::B32),
+                )),
+                Ok(FieldElementExpression::Number(Bn128Field::from(0)))
+            );
+        }
+
         #[test]
         fn if_else() {
             let mut propagator = ZirPropagator::default();