A hydrostatic axial piston machine has a drive shaft penetrating a housing on either side. In this case, the mechanically weaker of the two shaft ends is strengthened by an undercut being eliminated, said undercut defining the minimum diameter of the shaft end and thus of the entire drive shaft. Instead, the strength of the relevant shaft end is increased by a displacement of a circular bearing surface for a rolling bearing radially outwardly and away from the rolling bearing. In this case, the circular bearing surface is displaced below a compression spring which clamps the cylinder drum against a distributor plate. The resulting spacing between the circular bearing surface and the rolling bearing remaining in place is bridged by a sleeve or by a ring. A concave rounded shaft shoulder is simply formed below the sleeve and/or the ring.