A captive screw assembly for mounting in flat panels of widely varying thicknesses. The assembly includes an inverted hollow cup with an outwardly extending flange on its lower edge to engage a back surface of the panel and is temporarily held in place by outwardly-projecting spring tabs. A lower portion of the cup extends through the thickness of an aperture in the panel, while center and upper portions of the cup extend above a front surface of the panel. A cylindrical sleeve is seated over the cup, and a threaded screw extends through the sleeve and the cup. When the screw engages a threaded nut, positioned below the back surface of the panel, the head of the screw urges an upper edge of the sleeve downwardly and causes a lower edge of the sleeve to bear against a ring positioned around the exterior of the cup. When the screw is completely tightened, the panel is gripped between the lower cup flange and the ring.