A hybrid crane/rig mat that has outer side members of first and second side beams or boards of engineered lumber, oak or other hardwoods, or bumper members of solid or filled or unfilled hollow plastic members; a core structure of a metal or thermosetting plastic frame that includes side and end members and that contains therein a plurality of longitudinal members made of wood, engineered lumber, or of plastic or elastomeric materials; and a plurality of joining rods that pass through the outer side members, the core structure and longitudinal members to attach the outer side members to the core structure. The first end of the mat includes a male member and the second end of the mat includes a female member so that a first end of one mat can be releasably interlocked with a second end of a similarly configured and adjacently positioned additional mat.