A tappet of the pre-cited type with a separate anti-rotation device is known from DE 195 01 061 A1. This anti-rotation device comprises a needle roller that is retained radially inwards through a sheet metal element arranged on the inner peripheral surface of the skirt. The sheet metal element used as a “counter-holder” for the anti-rotation device unnecessarily increases the complexity and costs of the component. In addition, during operation of the tappet, there exists the danger that, with a widening of the sheet metal element, the anti-rotation device can migrate gradually in radially inward direction. In the worst case, a proper prevention of rotation of the tappet would not be guaranteed.