The invention relates to a hydrostatic axial piston machine, which has a compact construction with a high power-to weight ratio of several kW/kG, high overall efficiency higher than 90 % and considerably reduced working noise. Its working pressure exceeds 42 MPa and machine working as a pump is self-sucking. The machine in accordance with the invention is characterised in that the shaft (2) is equipped with an axial cam (6), which drives the elements controlling the working medium's flow between working chambers and the low- or high-pressure channels (12, 13) and with immovably attached on the shaft (2) support plate (3) with a fixed inclination angle, while the flow controlling element's shape is preferably a sleeve (9) with at least one hole (10) and a projection (11) supported on the cam's (6) running surface, and the internal surface of the sleeve (9) with at least one piston (5) head form together the working chamber.