A pump apparatus comprising a rotor drive mechanism configured to transfer rotation of a driving shaft to an external screw type rotor of a uniaxial eccentric screw pump via a connecting shaft, the driving shaft being rotated such that a center thereof is located at a fixed position, wherein: the driving shaft includes an inner space having an opening which is open toward the rotor, and the connecting shaft is inserted in the inner space; a base end portion of the connecting shaft is connected to the driving shaft, wherein the base end portion of the connecting shaft and the driving shaft are connected to each other via a second joint portion; a tip end portion of the connecting shaft is connected to the rotor, wherein the tip end portion of the connecting shaft and the rotor are connected to each other via a first joint portion, wherein the first and second joint portions (47, 48) and the connecting shaft are arranged in the inner space of the driving shaft, the inner space being sealed by a first seal portion (55, 69), the second joint portion is arranged on a radially inward side of a bearing portion configured to rotatably support the driving shaft; the first seal portion (55, 69) seals between an inner peripheral surface of the opening of the driving shaft and an outer peripheral surface of a base end portion of the rotor configured to carry out an eccentric rotational movement; the first seal portion (55, 69) deforms such that an inner wall portion thereof is able to move in a radial direction of the first seal portion (55, 69) and is formed such that the rotor is able to carry out the eccentric rotational movement; and a second seal portion seals between an outer peripheral surface of the opening of the driving shaft, the opening being open toward the rotor, and an inner peripheral surface of a casing of the uniaxial eccentric screw pump, characterized in that the first seal portion includes an outer side wall portion, an inner side wall portion, and a connecting wall portion, and the connecting wall portion connects a tip end portion of the outer side wall portion and a tip end portion of the inner side wall portion, the tip end portions being located at the side of the first seal portion facing the rotor. the driving shaft includes an inner space having an opening which is open toward the rotor, and the connecting shaft is inserted in the inner space; a base end portion of the connecting shaft is connected to the driving shaft, wherein the base end portion of the connecting shaft and the driving shaft are connected to each other via a second joint portion; a tip end portion of the connecting shaft is connected to the rotor, wherein the tip end portion of the connecting shaft and the rotor are connected to each other via a first joint portion, wherein the first and second joint portions (47, 48) and the connecting shaft are arranged in the inner space of the driving shaft, the inner space being sealed by a first seal portion (55, 69), the second joint portion is arranged on a radially inward side of a bearing portion configured to rotatably support the driving shaft; the first seal portion (55, 69) seals between an inner peripheral surface of the opening of the driving shaft and an outer peripheral surface of a base end portion of the rotor configured to carry out an eccentric rotational movement; the first seal portion (55, 69) deforms such that an inner wall portion thereof is able to move in a radial direction of the first seal portion (55, 69) and is formed such that the rotor is able to carry out the eccentric rotational movement; and a second seal portion seals between an outer peripheral surface of the opening of the driving shaft, the opening being open toward the rotor, and an inner peripheral surface of a casing of the uniaxial eccentric screw pump, characterized in that the first seal portion includes an outer side wall portion, an inner side wall portion, and a connecting wall portion, and the connecting wall portion connects a tip end portion of the outer side wall portion and a tip end portion of the inner side wall portion, the tip end portions being located at the side of the first seal portion facing the rotor.