diff --git a/naga/src/back/glsl/mod.rs b/naga/src/back/glsl/mod.rs
index fccbb5eec7..daca40b1db 100644
--- a/naga/src/back/glsl/mod.rs
+++ b/naga/src/back/glsl/mod.rs
@@ -1252,7 +1252,7 @@ impl<'a, W: Write> Writer<'a, W> {
         if global.space.initializable() && is_value_init_supported(self.module, global.ty) {
             write!(self.out, " = ")?;
             if let Some(init) = global.init {
-                self.write_const_expr(init)?;
+                self.write_global_const_expr(init)?;
             } else {
                 self.write_zero_init_value(global.ty)?;
             }
@@ -1788,6 +1788,13 @@ impl<'a, W: Write> Writer<'a, W> {
             // Write indentation (only for readability) and the type
             // `write_type` adds no trailing space
             write!(self.out, "{}", back::INDENT)?;
+
+            if let Some(init) = local.init {
+                if ctx.expr_kind_tracker.is_const(init) {
+                    write!(self.out, "const ")?;
+                }
+            }
+
             self.write_type(local.ty)?;
 
             // Write the local name
@@ -1897,7 +1904,7 @@ impl<'a, W: Write> Writer<'a, W> {
             self.write_array_size(base, size)?;
         }
         write!(self.out, " = ")?;
-        self.write_const_expr(constant.init)?;
+        self.write_global_const_expr(constant.init)?;
         writeln!(self.out, ";")?;
         Ok(())
     }
@@ -2648,12 +2655,30 @@ impl<'a, W: Write> Writer<'a, W> {
     ///
     /// [`Expression`]: crate::Expression
     /// [`Module`]: crate::Module
-    fn write_const_expr(&mut self, expr: Handle<crate::Expression>) -> BackendResult {
+    fn write_global_const_expr(&mut self, expr: Handle<crate::Expression>) -> BackendResult {
+        self.write_const_expr(expr, &self.module.global_expressions)
+    }
+
+    /// Write a const expression.
+    ///
+    /// Write `expr`, a handle to an [`Expression`] in the current [`Module`]'s
+    /// constant expression arena, as GLSL expression.
+    ///
+    /// # Notes
+    /// Adds no newlines or leading/trailing whitespace
+    ///
+    /// [`Expression`]: crate::Expression
+    /// [`Module`]: crate::Module
+    fn write_const_expr(
+        &mut self,
+        expr: Handle<crate::Expression>,
+        arena: &crate::Arena<crate::Expression>,
+    ) -> BackendResult {
         self.write_possibly_const_expr(
             expr,
-            &self.module.global_expressions,
+            arena,
             |expr| &self.info[expr],
-            |writer, expr| writer.write_const_expr(expr),
+            |writer, expr| writer.write_const_expr(expr, arena),
         )
     }
 
@@ -2720,7 +2745,7 @@ impl<'a, W: Write> Writer<'a, W> {
                 if constant.name.is_some() {
                     write!(self.out, "{}", self.names[&NameKey::Constant(handle)])?;
                 } else {
-                    self.write_const_expr(constant.init)?;
+                    self.write_global_const_expr(constant.init)?;
                 }
             }
             Expression::ZeroValue(ty) => {