The invention relates to a cup-shaped prosthesis shaft consisting of an air-tight and essentially rigid material comprising a sealing means for protecting against the entry of air from the proximal open side, said shaft being used in prostheses for replacing limbs. The inside of the shaft is provided with at least one pump device such that relative movements between the stump and the shaft during the use of the prosthesis pump air out of the inside of the prosthesis shaft via flow channels and monoway valves to the outside of the prosthesis shaft. The pump action is obtained by varying the volume of a compartment formed from flexible or elastic films, said compartment being arranged adjacently to the strump in the main extension thereof. The compartment is either fixed to the inner wall of a rigid prosthesis shaft, or built into the wall of a flexible and elastic removable stump coating which is arranged, as part of the prosthesis shaft, between the stump and a rigid frame.