A piston pump comprising: a cylinder having a cylinder chamber and a cutout part on the front end of the cylinder; a valve seat disposed in the cylinder, the valve seat having: a suction-side middle diameter portion internally fitted to the inner surface of the cylinder chamber; a reduced diameter portion formed in a taper shape, the reduced diameter portion disposed in a front side of the valve seat; a large diameter portion disposed between the suction-side middle diameter portion and the reduced diameter portion; a tapered portion formed between the large diameter portion and a discharge-side middle diameter portion; a cross-section enlarged portion formed between the large-diameter portion and the suction-side middle-diameter portion, the cross-section enlarged portion disposed in the cutout part with a clearance; a discharge flow passage having a inflow port on a rear side of the valve seat and a discharge port on a front end of the reduced diameter portion; a supply flow passage having a supply port and a suction port on a rear side of the valve seat; a flange member configured to hold the valve seat; the flange member including a through hole disposed in the flange member, the through hole having: a valve-seat internally disposing portion configured to fit the large-diameter portion; a tapered surface configured to fit the tapered portion; and a discharge-valve installation portion; a discharge valve disposed on the discharge port, the discharge valve having a valve body housing member being pipe-shaped, the valve body housing member internally disposed in the discharge-valve installation portion; a suction valve disposed on the suction port; and a packing; characterized in that the valve body housing member has a rear end configured to abut on the reduced diameter portion; the piston pump further comprises a packing installation portion, having a diameter smaller than that of the suction-side middle diameter portion, disposed on a rear-side of the suction-side middle diameter portion, wherein the packing is disposed in the packing installation portion. a cylinder having a cylinder chamber and a cutout part on the front end of the cylinder; a valve seat disposed in the cylinder, the valve seat having: a suction-side middle diameter portion internally fitted to the inner surface of the cylinder chamber; a reduced diameter portion formed in a taper shape, the reduced diameter portion disposed in a front side of the valve seat; a large diameter portion disposed between the suction-side middle diameter portion and the reduced diameter portion; a tapered portion formed between the large diameter portion and a discharge-side middle diameter portion; a cross-section enlarged portion formed between the large-diameter portion and the suction-side middle-diameter portion, the cross-section enlarged portion disposed in the cutout part with a clearance; a discharge flow passage having a inflow port on a rear side of the valve seat and a discharge port on a front end of the reduced diameter portion; a supply flow passage having a supply port and a suction port on a rear side of the valve seat; a suction-side middle diameter portion internally fitted to the inner surface of the cylinder chamber; a reduced diameter portion formed in a taper shape, the reduced diameter portion disposed in a front side of the valve seat; a large diameter portion disposed between the suction-side middle diameter portion and the reduced diameter portion; a tapered portion formed between the large diameter portion and a discharge-side middle diameter portion; a cross-section enlarged portion formed between the large-diameter portion and the suction-side middle-diameter portion, the cross-section enlarged portion disposed in the cutout part with a clearance; a discharge flow passage having a inflow port on a rear side of the valve seat and a discharge port on a front end of the reduced diameter portion; a supply flow passage having a supply port and a suction port on a rear side of the valve seat; a flange member configured to hold the valve seat; the flange member including a through hole disposed in the flange member, the through hole having: a valve-seat internally disposing portion configured to fit the large-diameter portion; a tapered surface configured to fit the tapered portion; and a discharge-valve installation portion; a valve-seat internally disposing portion configured to fit the large-diameter portion; a tapered surface configured to fit the tapered portion; and a discharge-valve installation portion; a discharge valve disposed on the discharge port, the discharge valve having a valve body housing member being pipe-shaped, the valve body housing member internally disposed in the discharge-valve installation portion; a suction valve disposed on the suction port; and a packing; characterized in that the valve body housing member has a rear end configured to abut on the reduced diameter portion; the piston pump further comprises a packing installation portion, having a diameter smaller than that of the suction-side middle diameter portion, disposed on a rear-side of the suction-side middle diameter portion, wherein the packing is disposed in the packing installation portion.