A switchable cup tappet for a valve timing mechanism of an internal combustion engine, which has a cup basic body with an annular base loaded by large-lift cams. A hollow-cylindrical projection protrudes from an inner edge of the base and an inner body extends in the hole of the projection. The disc-like base is contacted by a small-lift cam. In a hole of the inner body two coupler pistons are coupled in sections with a driver surface of the cup basic body for a large valve stroke. The small stroke occurs by complete displacement into the radial hole. An annular web, spaced from its end faces at both ends, is attached integrally, in which the radial hole extends with the coupler pistons. The driver surface for the pistons is formed by a lower edge of the projection, which is spaced from the bases.