A hydrostatic axial piston machine includes a cylinder drum having a substantially hollow cylindrical base body, and liners. The body includes cylinder bores located around a central axis. The liners have an outer diameter press-fitted into the bores such that an outer end face of each liner is positioned in a region of an opening of a respective bore, and such that an inner end face of each liner is positioned deep within the respective bore. An outer half of each liner, starting from the outer end face, includes an axially delimited circumferential recess in an outer casing surface of the liner. The machine is configured to operate with great forces acting between the liners and displacement pistons. The recess in each liner is shaped such that, in an axial section through the liner enclosing an axis of the liner, a depth of the recess increases more than once and decreases more than once.