diff --git a/lisp/progmodes/sh-script.el b/lisp/progmodes/sh-script.el
index aa6ada96cd4..ae90531a7fe 100644
--- a/lisp/progmodes/sh-script.el
+++ b/lisp/progmodes/sh-script.el
@@ -1625,9 +1625,9 @@ with your script for an edit-interpret-debug cycle."
   (setq-local defun-prompt-regexp
               (concat
                "^\\("
-               "\\(function[ \t]\\)?[ \t]*[[:alnum:]]+[ \t]*([ \t]*)"
+               "\\(function[ \t]\\)?[ \t]*[[:alnum:]_]+[ \t]*([ \t]*)"
                "\\|"
-               "function[ \t]+[[:alnum:]]+[ \t]*\\(([ \t]*)\\)?"
+               "function[ \t]+[[:alnum:]_]+[ \t]*\\(([ \t]*)\\)?"
                "\\)[ \t]*"))
   (setq-local add-log-current-defun-function #'sh-current-defun-name)
   (add-hook 'completion-at-point-functions