Golf club heads include a face member with a face having a striking surface and a rear side opposite the striking surface, where a rear cavity is defined on the rear side of the face member, and a rear member is connected to the rear side of the face member, such that the rear member is at least partially received within the rear cavity. A resilient material is positioned between the rear member and the face member, and the head also includes an engagement member rigidly engaging the face member and the rear member at a point between the heel edge and the toe edge of the rear member. The engagement member has a rigidity greater than that of the resilient material and may form a sole area of rigid engagement between the face member and the rear member.