In a syringe type pump with a barrel (2) and a piston (4) movable in the interior of the barrel the barrel has the shape of a segment of a toroidal tube (2) and the piston is moved by means of a driving rod (6) which is guided and supported by the inner surface of the barrel wall. By the toroidal shape the overall size of the pump is significantly reduced and by guiding and supporting the driving rod of the piston by the inner surface of the barrel wall intrinsic problems of tightness, stick- slip phenomena and blockage are solved. A device for injecting fluid into a patient"s body or removing body fluid therefrom is using a syringe type pump with a toroidal barrel and a driving rod of the piston guided and supported by the inner surface of the barrel wall.