A paper stack press machine comprising: a base having a flat press surface for support of a front or back side of a paper stack; a rectangular or square pressing plate arranged opposite the press surface so as to be movable toward and away from the press surface and having first and second sides opposed to each other; a pressing plate drive mechanism moving the pressing plate in a direction perpendicular to the press surface between a standby position at which the pressing plate separates from the paper stack on the press surface and a press position at which the pressing plate presses the paper stack against the press surface, characterized in that a surface of the pressing plate which faces the press surface being elastically deformable in a manner such that the surface of the pressing plate is inclined or curved so as to be gradually away from the press surface from the first side toward the second side of the pressing plate when the pressing plate takes the standby position, and the surface of the pressing plate gradually contacts the paper stack on the press surface from the first side toward the second side of the pressing plate while the pressing plate moves from the standby position to the press position, and the surface of the pressing plate is flat and parallel to the press surface when the pressing plate takes the press position; a pushing bar extending in a direction perpendicular to the press surface at the second side of the pressing plate and opposed to the press surface at a head thereof; and a pushing bar drive mechanism moving the pushing bar in an axial direction of the pushing bar between a retracted position at which the head of the pushing bar separates from the paper stack on the press surface and an advanced position at which the head of the pushing bar pushes the paper stack against the press surface, wherein the paper stack press machine is configured such that, when the paper stack is placed on the press surface, and the pushing bar moves from the retracted position to the advanced position after the pressing plate moves from the standby position to the press position, thereafter the pushing bar moves from the advanced position to the retracted position after the pressing plate moves from the press position to the standby position. a base having a flat press surface for support of a front or back side of a paper stack; a rectangular or square pressing plate arranged opposite the press surface so as to be movable toward and away from the press surface and having first and second sides opposed to each other; a pressing plate drive mechanism moving the pressing plate in a direction perpendicular to the press surface between a standby position at which the pressing plate separates from the paper stack on the press surface and a press position at which the pressing plate presses the paper stack against the press surface, characterized in that a surface of the pressing plate which faces the press surface being elastically deformable in a manner such that the surface of the pressing plate is inclined or curved so as to be gradually away from the press surface from the first side toward the second side of the pressing plate when the pressing plate takes the standby position, and the surface of the pressing plate gradually contacts the paper stack on the press surface from the first side toward the second side of the pressing plate while the pressing plate moves from the standby position to the press position, and the surface of the pressing plate is flat and parallel to the press surface when the pressing plate takes the press position; a pushing bar extending in a direction perpendicular to the press surface at the second side of the pressing plate and opposed to the press surface at a head thereof; and a pushing bar drive mechanism moving the pushing bar in an axial direction of the pushing bar between a retracted position at which the head of the pushing bar separates from the paper stack on the press surface and an advanced position at which the head of the pushing bar pushes the paper stack against the press surface, wherein the paper stack press machine is configured such that, when the paper stack is placed on the press surface, and the pushing bar moves from the retracted position to the advanced position after the pressing plate moves from the standby position to the press position, thereafter the pushing bar moves from the advanced position to the retracted position after the pressing plate moves from the press position to the standby position.