A radial piston pump (1) for supplying fuel at high-pressure to an internal combustion engine has a displacement housing (3) equipped with a compression chamber (4), a reciprocating piston which is arranged in a cylinder chamber (5) of a cylinder (30), a suction valve (10) which is connected to a fuel supply line (8) and a pressure valve (12) which is connected to a fuel outlet line (14). The suction valve (10) and the pressure valve (12) have, respectively, a closing head (16, 16'), a valve seat (18, 18'), a cylinder section (20, 20') and springs (22, 22'). The suction valve (10) and the pressure valve (12) are identical components and the pressure valve (12) is incorporated into the radial piston pump (1) in the direction of flow counter to the suction valve (10).