The pump has a housing (2) with multiple cylinder bores (3) for pistons (4) driven by an eccentric. There is a pressure chamber (15) in the piston over a valve assembly (11,3,14) with a consumer connected to it. The piston induces pressure fluid to its upper surface from an annular chamber (17). The flow of pressure fluid passes from the annular chamber over the pistons arranged flow opening (21) in a sealing disc (20) and over a further channel connection in the piston pressure chamber. The channel connection can be formed as an annular suction duct (15) and the flow opening can have guide plates extending into the suction duct (18).