The pump is of an axial flow rotary type suitable for implantation into the human heart or vascular system. The pump has an elongate tubular casing (1) including an electric motor (4) and defining an inlet (2) for blood, an outlet (3) for blood longitudinally spaced from the inlet and a substantially axial blood flow path (8) from the inlet to the outlet. An elongate rotatable element (7) is arranged to fit within the casing with spacing (15) between an outer surface of the rotatable element and an inner surface of the casing; the rotatable element comprises an electric motor rotor portion (10) arranged to be driven by the electric motor stator and a primary substantially axial blood flow path along the inside of the rotatable element. A rotary impeller (11) is provided axially spaced from the rotor portion for impelling blood along the primary flow path.