A face or face insert (40) for a golf club head (20) is disclosed herein. The face (40) has an interior surface (40a) with a first thickness section (200) and a second thickness region (205). The first thickness section (200) preferably has a thickness that is at least 0.025 inch greater than the thickness of the second thickness region (205). In a most preferred embodiment, the first thickness section (205) has an H shape. The face or face insert (40) with variable thickness allows for a face or face insert (40) with less mass in a golf club head (20) that conforms to the United States Golf Association regulations.