A hydrostatic axial piston machine, in particular a swashplate machine, has a cylinder drum (3) mounted so that it can rotate around an axis of rotation (2). The cylinder drum (3) is provided with cylinder bores (4), in each of which a piston (5) is mounted so that it can be displaced longitudinally. The cylinder drum (3) is axially supported on a control surface (8) affixed to the casing and on which an inlet connection (10) and an outlet connection (11) are realized. The cylinder bores (4) can each be placed in communication by a connecting channel (12) with the control surface (8). The connecting channel (12) is provided with a cross-section that increases from the cylinder bore (4) toward the control surface (8).