A mine prop provided with an overpressure valve of large flow-through section which opens when excessive forces suddenly act on the prop to discharge pressure fluid from the interior of the prop. The overpressure valve comprises a hollow cylindrical housing forming at one end a valve seat communicating with the fluid-filled inner space of the prop and a valve member axially guided in the housing for movement between a closed position engaging the valve seat and an open position. The fluid-filled space of the prop communicates with channels leading to the outside of the prop. The valve member is normally maintained in the closed position by a gas pillow under high pretension confined in a pressure space delimited peripherally by the wall of the valve housing and at opposite ends respectively by the valve member and a plug fluid tightly mounted in and closing the other end of the housing. The valve member and the plug are both formed from metal and are both provided at facing ends with annular slender sealing lips of triangular cross-section tapering toward each other, the outer surfaces of which are pressed into engagement with the inner peripheral surface of the housing by the pressure of the gas pillow.