An implantable aortic blood pump includes a rigid body having wall extending along a long axis and defining an inflation port portion with an inflation aperture therethrough. The aperture is fluid communication with an inner surface of the body and on a fluid supply, the body is preferably independent of an external brace or an external stiffener, yet still has a cantilevered deformation of less than 8 millimeters in response to a 200 gram weight suspended from a front body edge. A deflecting structure of a membrane deflects in response to fluid pressure so as to pump blood when the pump is secured to a subject aorta.