An axial plunger pump or motor of the type such that a valve plate having a suction port and a discharge port drilled therein is fixed to a casing in which a rotary shaft is mounted. A cylinder block having one end surface opposed to the valve plate is coupled to the rotary shaft. A plurality of bores whose one ends can be communicated with the suction port and the discharge port are drilled in the cylinder block in parallel to the rotary shaft. A plurality of plungers, which can reciprocate within the respective bores in accordance with rotation of the rotary shaft are slidably fitted in the bores on the side of the other ends. A seal plate positioned between the valve plate and the cylinder block and making slide contact with the valve plate is coupled to the rotary shaft. A plurality of bushes or bushings, each consisting of a thin-walled cylinder portion fitted in one end portion of the bore and capable of making tight contact with an inner wall surface of the bore as expanded in diameter by a high-pressure liquid within the bore and a flange portion butting against the seal plate, are interposed between the seal plate and the cylinder block. An urging member for bringing the flange portion of the bush into tight contact with the seal plate in cooperation with the high-pressure liquid is provided between the flange portion of the bush and the one end surface of the cylinder block.