A resiliently yieldable tail stock device for use in a numerically controlled lathe comprises a body slidable along a bed toward and away from a spindle, the slidable body having a bore and a passage hole each formed therethrough in an axial alignment with the spindle. Removably received within the bore of the slidable body is a center socket movable between an extended position and a retracted position and having a tapering blind bore open at its front end. The center socket carries a live center that has a pointed front end engageable with a workpiece and a tapering rear shank fitted into the tapering bore. Fixedly secured to the center socket is an elongate rod carrying a dog at its distal end. A compression spring is used to resiliently bias the center socket toward the extended position. A combination of electric motor and lead screw serves to cause a linear reciprocating movement of the slidable body. The electric motor is deenergized as the dog reaches a rearmost position just above a proximity switch.