diff --git a/src/Expr.cc b/src/Expr.cc
index 19b29fb521..7ba9559509 100644
--- a/src/Expr.cc
+++ b/src/Expr.cc
@@ -51,6 +51,8 @@ const char* expr_name(ExprTag t)
 		"&",
 		"|",
 		"^",
+		"<<",
+		">>",
 		"&&",
 		"||",
 		"<",
@@ -957,6 +959,12 @@ ValPtr BinaryExpr::Fold(Val* v1, Val* v2) const
 		case EXPR_XOR:
 			DO_UINT_FOLD(^);
 			break;
+		case EXPR_LSHIFT:
+			DO_INT_FOLD(<<);
+			break;
+		case EXPR_RSHIFT:
+			DO_INT_FOLD(>>);
+			break;
 
 		case EXPR_AND_AND:
 			DO_INT_FOLD(&&);
@@ -2156,7 +2164,22 @@ BitExpr::BitExpr(ExprTag arg_tag, ExprPtr arg_op1, ExprPtr arg_op2)
 	if ( IsVector(bt2) )
 		bt2 = t2->AsVectorType()->Yield()->Tag();
 
-	if ( (bt1 == TYPE_COUNT) && (bt2 == TYPE_COUNT) )
+	if ( tag == EXPR_LSHIFT || tag == EXPR_RSHIFT )
+		{
+		if ( IsIntegral(bt1) && bt2 == TYPE_COUNT )
+			{
+			if ( is_vector(op1) || is_vector(op2) )
+				SetType(make_intrusive<VectorType>(base_type(bt1)));
+			else
+				SetType(base_type(bt1));
+			}
+		else if ( IsIntegral(bt1) && bt2 == TYPE_INT )
+			ExprError("requires \"count\" right operand");
+		else
+			ExprError("requires integral operands");
+		}
+
+	else if ( (bt1 == TYPE_COUNT) && (bt2 == TYPE_COUNT) )
 		{
 		if ( is_vector(op1) || is_vector(op2) )
 			SetType(make_intrusive<VectorType>(base_type(TYPE_COUNT)));
diff --git a/src/Expr.h b/src/Expr.h
index 4e32097dfc..9cffbabd3f 100644
--- a/src/Expr.h
+++ b/src/Expr.h
@@ -53,6 +53,8 @@ enum ExprTag : int
 	EXPR_AND,
 	EXPR_OR,
 	EXPR_XOR,
+	EXPR_LSHIFT,
+	EXPR_RSHIFT,
 	EXPR_AND_AND,
 	EXPR_OR_OR,
 	EXPR_LT,
diff --git a/src/parse.y b/src/parse.y
index 252b7390e2..d1ee9972c8 100644
--- a/src/parse.y
+++ b/src/parse.y
@@ -5,7 +5,7 @@
 // Switching parser table type fixes ambiguity problems.
 %define lr.type ielr
 
-%expect 195
+%expect 199
 
 %token TOK_ADD TOK_ADD_TO TOK_ADDR TOK_ANY
 %token TOK_ATENDIF TOK_ATELSE TOK_ATIF TOK_ATIFDEF TOK_ATIFNDEF
@@ -46,6 +46,7 @@
 %left '|'
 %left '^'
 %left '&'
+%left TOK_LSHIFT TOK_RSHIFT
 %left '+' '-'
 %left '*' '/' '%'
 %left TOK_INCR TOK_DECR
@@ -554,6 +555,18 @@ expr:
 			$$ = new BitExpr(EXPR_XOR, {AdoptRef{}, $1}, {AdoptRef{}, $3});
 			}
 
+	|	expr TOK_LSHIFT expr
+			{
+			set_location(@1, @3);
+			$$ = new BitExpr(EXPR_LSHIFT, {AdoptRef{}, $1}, {AdoptRef{}, $3});
+			}
+
+	|	expr TOK_RSHIFT expr
+			{
+			set_location(@1, @3);
+			$$ = new BitExpr(EXPR_RSHIFT, {AdoptRef{}, $1}, {AdoptRef{}, $3});
+			}
+
 	|	expr TOK_AND_AND expr
 			{
 			set_location(@1, @3);
diff --git a/src/scan.l b/src/scan.l
index 0f0efe4f2d..17c07c9749 100644
--- a/src/scan.l
+++ b/src/scan.l
@@ -248,6 +248,9 @@ ESCSEQ	(\\([^\r\n]|[0-7]+|x[[:xdigit:]]+))
 "&&"	return TOK_AND_AND;
 "||"	return TOK_OR_OR;
 
+"<<"	return TOK_LSHIFT;
+">>"	return TOK_RSHIFT;
+
 add	return TOK_ADD;
 addr	return TOK_ADDR;
 any	return TOK_ANY;
diff --git a/src/script_opt/CPP/Exprs.cc b/src/script_opt/CPP/Exprs.cc
index 6c0912d2db..f8336b9365 100644
--- a/src/script_opt/CPP/Exprs.cc
+++ b/src/script_opt/CPP/Exprs.cc
@@ -89,6 +89,10 @@ string CPPCompile::GenExpr(const Expr* e, GenType gt, bool top_level)
 			return GenBinary(e, gt, "|", "or");
 		case EXPR_XOR:
 			return GenBinary(e, gt, "^", "xor");
+		case EXPR_LSHIFT:
+			return GenBinary(e, gt, "<<", "lshift");
+		case EXPR_RSHIFT:
+			return GenBinary(e, gt, ">>", "rshift");
 		case EXPR_AND_AND:
 			return GenBinary(e, gt, "&&", "andand");
 		case EXPR_OR_OR:
diff --git a/src/script_opt/Expr.cc b/src/script_opt/Expr.cc
index 36a7a2267e..d893431e66 100644
--- a/src/script_opt/Expr.cc
+++ b/src/script_opt/Expr.cc
@@ -257,6 +257,8 @@ bool Expr::IsFieldAssignable(const Expr* e) const
 		case EXPR_AND:
 		case EXPR_OR:
 		case EXPR_XOR:
+		case EXPR_LSHIFT:
+		case EXPR_RSHIFT:
 		case EXPR_FIELD:
 		case EXPR_HAS_FIELD:
 		case EXPR_IN:
@@ -1293,7 +1295,7 @@ bool BitExpr::WillTransform(Reducer* c) const
 
 ExprPtr BitExpr::Reduce(Reducer* c, StmtPtr& red_stmt)
 	{
-	if ( GetType()->Tag() != TYPE_COUNT )
+	if ( ! IsIntegral(GetType()->Tag()) )
 		return BinaryExpr::Reduce(c, red_stmt);
 
 	auto zero1 = op1->IsZero();
@@ -1311,7 +1313,7 @@ ExprPtr BitExpr::Reduce(Reducer* c, StmtPtr& red_stmt)
 		if ( Tag() == EXPR_AND )
 			return zero_op->ReduceToSingleton(c, red_stmt);
 		else
-			// OR or XOR
+			// OR or XOR or LSHIFT or RSHIFT
 			return non_zero_op->ReduceToSingleton(c, red_stmt);
 		}
 
diff --git a/testing/btest/Baseline/language.count/out b/testing/btest/Baseline/language.count/out
index fb316ea55c..0d1b3cab6a 100644
--- a/testing/btest/Baseline/language.count/out
+++ b/testing/btest/Baseline/language.count/out
@@ -20,6 +20,8 @@ bitwise and (PASS)
 bitwise or (PASS)
 bitwise or (PASS)
 bitwise xor (PASS)
+bitwise lshift (PASS)
+bitwise rshift (PASS)
 bitwise complement (PASS)
 bitwise complement (PASS)
 max count value = 18446744073709551615 (PASS)
diff --git a/testing/btest/Baseline/language.int/out b/testing/btest/Baseline/language.int/out
index d7924ec012..b2f4f2c04a 100644
--- a/testing/btest/Baseline/language.int/out
+++ b/testing/btest/Baseline/language.int/out
@@ -18,6 +18,7 @@ modulus operator (PASS)
 division operator (PASS)
 assignment operator (PASS)
 assignment operator (PASS)
+bitwise rshift (PASS)
 max int value = 9223372036854775807 (PASS)
 min int value = -9223372036854775808 (PASS)
 max int value = 9223372036854775807 (PASS)
diff --git a/testing/btest/language/count.zeek b/testing/btest/language/count.zeek
index ca683598ac..7ba4c7982f 100644
--- a/testing/btest/language/count.zeek
+++ b/testing/btest/language/count.zeek
@@ -49,6 +49,8 @@ event zeek_init()
 	test_case( "bitwise or", c2 | 0x4 == c2 );
 	test_case( "bitwise or", c4 | 0x4 == c4 );
 	test_case( "bitwise xor", c4 ^ 0x4 == 251 );
+	test_case( "bitwise lshift", c4 << 0x4 == 4080 );
+	test_case( "bitwise rshift", c4 >> 0x4 == 15 );
 	test_case( "bitwise complement", ~c6 == 0 );
 	test_case( "bitwise complement", ~~c4 == c4 );
 
diff --git a/testing/btest/language/int.zeek b/testing/btest/language/int.zeek
index c9344dd007..1f010e8048 100644
--- a/testing/btest/language/int.zeek
+++ b/testing/btest/language/int.zeek
@@ -54,6 +54,7 @@ event zeek_init()
 	test_case( "assignment operator", i2 == 7 );
 	i2 -= 2;
 	test_case( "assignment operator", i2 == 5 );
+	test_case( "bitwise rshift", i10 >> 1 == -6 );
 
 	# Max/min value tests