A rail clamp mount that may be quickly and easily firmly secured to a rail, such as a rail carried by a gun, and that may be quickly and easily released from the rail. A preferred embodiment comprises a mount base including a first rail-engaging surface; a generally U-shaped, somewhat elastic clamping member carried by the mount base and including two second rail-engaging surfaces at the ends of the legs of the U, and a third second rail-engaging surface at the end of the center section of the clamping member between the legs of the U, the second rail-engaging surfaces being opposed to and transversely spaced from the first rail-engaging surface; a cam mechanism mounting the clamping member to the mount base for imparting transverse movement to the clamping member when actuated; and an actuator for the cam mechanism including a throw handle.