A mechanical system, comprising a tappet including a body, a support element defining two bores centered on a first axis, a pin comprising two opposite ends each adapted to be fitted in one of the two bores, and a roller element positioned between the two bores along the first axis and movable in rotation relative to the pin around the first axis. The support element is distinct from the body and fixed thereto, and the support element also comprises at least one antirotation device integrally formed thereto. The mechanical system can be integrated into an injection pump and/or a valve actuator.