The invention concerns a hydraulic axial piston machine (1) with a cylinder body (3), at least one piston (9) to be axially displaceable in the cylinder body (3), said piston (9) resting on a swash plate (13) by way of a slide shoe (11), with a pressure plate (14) loading the slide shoe (11) in the direction of the swash plate (13), and a hold-down part (16), which bears with a contact surface (18) on a counter surface (20) of the pressure plate(14) facing away from the swash plate (13). It is endeavored to operate the machine with as little wear as possible. For this purpose, it is ensured that the contact surface (18) is formed by a circumferential surface section of a cone, whose peak (19) is directed towards the swash plate (13).