A switchable valve drive element of an internal combustion engine can be actuated hydraulically. A valve tappet which can be displaced axially in a bore of the machine housing by the cam of a camshaft. A switching duct adjoins the valve tappet and is filled with a hydraulic oil. A connection on the valve drive element between the switching duct and a space with a lower pressure level compared to the pressure in the switching duct. The connection can be produced between the switching duct and the space with a lower pressure level by means of the valve tappet. The space may be inside the tappet.