A uniaxial eccentric screw pump including: a male thread-like rotor directly coupled to a driving shaft; a stator rotatably supported via a sliding bearing, the sliding bearing formed of at least one of a self-lubricating bearing (5, 6) or a submerged bearing and the stator having a female thread-like inner surface and an axis of rotation eccentrically disposed with respect to an axis of rotation of the rotor, wherein a fluid is pumped from an intake side to a discharge side while the rotor is rotating eccentrically moving with respect to a shaft center of the stator, the pump being characterized by comprising: a first annular small-diameter portion axially extending toward the discharge side from an end of the discharge side of the stator; a first seal member in a sliding contact with a circumferential surface of the first annular small-diameter portion to hermetically seal an end of the sliding bearing and the stator at the discharge side; a second annular small-diameter portion axially extending toward the intake side from the other axially extending toward the intake side from the other end of the intake side of the stator; and a second seal member in sliding contact with the circumferential surface of the second annular small-diameter portion to hermetically seal an end of a bearing slidingly contacting portion and the stator at the intake side, wherein an external diameter (φA) of the first annular small-diameter portion is smaller than an external diameter (φB) of the bearing slidingly contacting portion at the intake side of the stator,and an area of the first annular small-diameter portion and an opening of the first annular small-diameter portion, when viewed in an axial direction, is larger than an area of the opening of the discharge side of the stator (4 when viewed in the axial direction. a male thread-like rotor directly coupled to a driving shaft; a stator rotatably supported via a sliding bearing, the sliding bearing formed of at least one of a self-lubricating bearing (5, 6) or a submerged bearing and the stator having a female thread-like inner surface and an axis of rotation eccentrically disposed with respect to an axis of rotation of the rotor, wherein a fluid is pumped from an intake side to a discharge side while the rotor is rotating eccentrically moving with respect to a shaft center of the stator, the pump being characterized by comprising: a first annular small-diameter portion axially extending toward the discharge side from an end of the discharge side of the stator; a first seal member in a sliding contact with a circumferential surface of the first annular small-diameter portion to hermetically seal an end of the sliding bearing and the stator at the discharge side; a second annular small-diameter portion axially extending toward the intake side from the other axially extending toward the intake side from the other end of the intake side of the stator; and a second seal member in sliding contact with the circumferential surface of the second annular small-diameter portion to hermetically seal an end of a bearing slidingly contacting portion and the stator at the intake side, wherein an external diameter (φA) of the first annular small-diameter portion is smaller than an external diameter (φB) of the bearing slidingly contacting portion at the intake side of the stator,and an area of the first annular small-diameter portion and an opening of the first annular small-diameter portion, when viewed in an axial direction, is larger than an area of the opening of the discharge side of the stator (4 when viewed in the axial direction. a first annular small-diameter portion axially extending toward the discharge side from an end of the discharge side of the stator; a first seal member in a sliding contact with a circumferential surface of the first annular small-diameter portion to hermetically seal an end of the sliding bearing and the stator at the discharge side; a second annular small-diameter portion axially extending toward the intake side from the other axially extending toward the intake side from the other end of the intake side of the stator; and a second seal member in sliding contact with the circumferential surface of the second annular small-diameter portion to hermetically seal an end of a bearing slidingly contacting portion and the stator at the intake side, wherein an external diameter (φA) of the first annular small-diameter portion is smaller than an external diameter (φB) of the bearing slidingly contacting portion at the intake side of the stator,and an area of the first annular small-diameter portion and an opening of the first annular small-diameter portion, when viewed in an axial direction, is larger than an area of the opening of the discharge side of the stator (4 when viewed in the axial direction.