Abstract: A hydraulic radial piston pump having a plurality of pistons arranged radially around the rotary shaft for sequential reciprocating motion in which working oil is introduced from the inner oil chamber in the pump casing supporting the rotary shaft and pistons passed into the outer oil chambers provided behind the pistons and then, discharged from these outer oil chambers to delivery passages. A eccentric motion element, the outer periphery of which abuts on the head of each piston, is connected to the rotary shaft by connecting means so that the eccentric motion element can perform eccentric movements about the rotary shaft. The eccentric motion element is also prevented by rotation stopper means from rotating about the rotary shaft. The piston has a suction orifice provided in the head thereof which is yieldingly pressed against the outer periphery of the eccentric motion element by spring means.