A radial piston pump for generation of high fuel pressures in fuel injection systems comprises a pump housing, a pump shaft and at least one cylinder insert, arranged radially to the pump shaft. A cylinder chamber is located within the cylinder insert in which a piston can move back and forth. The cylinder insert is connected with a front face to a flattening of the pump housing, by connecting means. The cylinder insert comprises an inlet port and a high pressure port. The front face of the cylinder insert and/or the flattening of the pump housing comprise precisely machined raised sealing regions for sealing the cylinder insert against the pump housing, which are relatively small in relation to the total front face of the cylinder insert and the total flattening of the pump housing. A high surface pressure is thus achieved in the sealing region.