An axial variable capacity rotary pump which yields a stepless change of capacity. The pump has a casing with an inlet and outlet, at least one rotary member with engaging elements mounted on the periphery of the rotary member for engaging a mating member, and a pair of axial sealing element which seal either axial side of the rotary member. One sealing element moves together with the rotary member axially to change a length of a sealed working chamber between the members, thereby changing the delivery capacity per revolution of the pump.