A linear valve drive for connection to a valve body having a valve seat and at least one flow passage with at least one inlet and at least one outlet, comprises a drive housing with a drive unit accommodated therein, an actuating element axially shiftable by the drive unit and coupled with a valve closing element to be pressed against the valve seat, and optionally closing the flow passage, and a supporting unit surrounding the actuating element, which is designed to be attached to the valve body. A spring system loaded by actuating the linear valve drive is provided at the supporting unit, which in dependence on the compression path has different spring rates. Furthermore, a correspondingly equipped valve is described.