A golf club head is described having a club head body having an external surface with a heel portion, a toe portion, a crown portion, a sole portion, and a front opening. The golf club head also includes a face insert support structure located at the front opening. The support structure includes a rear support member. The rear support member includes a support portion interior surface contour defining an apex point and an undercut distance in an undercut region within at least one major or minor plane. A non-undercut region is located in at least one major or minor plane intersecting the crown to face transition region.