In one embodiment described in the specification, a surgically implantable reciprocating pump employs a check valve as the piston, which is driven by a permanent magnet linear electric motor to assist either side of the natural heart. The pump is implanted in the aorta or pulmonary artery using vascular attachment cuffs such as flexible cuffs for suturing at each end with the pump output directly in line with the artery. The pump is powered by surgically implanted rechargeable batteries. In another embodiment, pairs of pumps are provided to replace or assist the natural heart or to provide temporary blood flow throughout the body, for example, during operations to correct problems with the natural heart.