A hydrostatic axial piston machine includes a housing and a pivot cradle. At least one slide bearing of the pivot cradle on a high-pressure side is hydrostatically relieved. The slide bearing includes one or two pairs of relief grooves. A relief pressure field develops about and between the one or two pairs of relief grooves as the grooves are supplied with relief pressure medium on one side and are closed at their outer ends. An optional slide bearing on a low-pressure side has one or two limiting grooves which delimit the relief pressure field there, as the limiting grooves are open at their outer ends.