The pump housing (39) has an inner space for accommodating a pump rotor (10) which is transferred from radially compressed state to the radially expanded state. A reinforcing element (29) is rotated in the circumferential direction of housing skin that is stretched by expansion of reinforcing element in the fully expanded condition of housing. A low stretch element (37) rotated in circumferential direction, is stretched less than 5% in the expanded state as opposed to the force-free state in circumferential direction, and limits expansion of pump housing in radial direction. An independent claim is included for fluid pump.