Abstract: This invention relates to a hydrostatic axial piston machine that utilizes a swash plate construction with a plurality of axially movable pistons mounted in a cylinder drum. The pistons are each supported on a slide face by individual sliding blocks and are hydrostatically compensated. Each sliding block has a sliding block plate facing the slide face, and is in communication on the side opposite the sliding block plate with a piston. A sealing web is formed on the sliding block plate and the sliding block is provided with a bore that leads from the piston side to the slide face side. The sealing web on the sliding block plate of the sliding block is realized in the form of a substantially concave surface. In one configuration, the concave surface, starting from an outside periphery of the sliding block, extends substantially to the vicinity of the bore.