An actuator module including a piezoactuator, for example for a piezoinjector for metering fuel in an internal combustion engine, is proposed. The piezoactuator has piezoelements stacked one above another between an actuator head and an actuator foot and is provided with at least one elastomer layer enclosing the piezoelements. The elastomer layer is enveloped by a corrugated bellows or by telescopic tubes, composed of a material that is diffusion-impermeable with respect to a fuel to be metered by the piezoinjector. The corrugated bellows or the telescopic tubes have on their periphery grooves which can absorb expansions of the elastomer layer or of the piezoactuator.