A ventricular assist device includes a pump such as an axial flow pump, an outflow cannula connected to the outlet of the pump, and an anchor element. The anchor element is physically connected to the pump, as by an elongate element. The pump is implanted within the left ventricle with the outflow cannula projecting through the aortic valve but desirably terminating short of the aortic arch. The anchor element is fixed to the wall of the heart near the apex of the heart so that the anchor element holds the pump and outflow cannula in position.