In the casing (1) of the proposed axial-piston machine is located a cylinder block (2) with cavities (10). The axes of the cavities (10) are parallel to the longitudinal axis (01-01) of the shaft (11) and pistons (12) are mounted inside said cavities with the possibility of reciprocating movement. Each of the pistons (12) is hingedly connected to one end (14a) of a rod (14). The other end (14b) of the rod (14) is hingedly connected to a sloped washer (15) which is mounted by means of a first support (22) on a sloped neck (23) of the shaft (11) mounted on supports in the casing (1) and which is hingedly connected by means of universal couplings (34 and 35) to the casing (1). The machine is further provided with a second, spherically shaped support (49) of the sloped washer (15). The support (49) is connected to the casing (1) and its centre (03) coincides essentially with the geometrical centre of a coupling element (47) of the universal couplings (34 and 35). Through the centre (03) passes a bisector plane (p-p) constituting the symmetry plane of the universal couplings (34 and 35).