A vise assembly has a pair of moveable jaws mounted on guideways for movement toward and away from each other. The moveable jaws are driven by a vise screw on the vise body through head members of a pair of jaw nuts. The head members fit into cavities on the underside of the moveable jaws and have projections on first ends that have surfaces engaging mating recessed surfaces formed on one end of the cavities. Adjustable plungers are mounted on the head members and are extendable outwardly from a second end of the head members to engage and drive against surfaces of the cavities in a second direction. The adjustable plungers are adjustable in length so they can be retracted into mounting bores in the head members so the moveable jaws can be mounted on and removed from the head members, and extended so driving surfaces of projections on the head members and of the plungers are both in engagement with surfaces of the cavities.