Abstract The basic shape of the outer surface (8) of the prosthesis and the envelopes (9) of the screw thread (7) form, in cross-section, the branch of a hyperbola whose axis of symmetry (11 or 12) encloses, with the equatorial plane of the cup, an angle ( alpha ) of between 48 DEG and 58 DEG . On the one hand, the hyperbola shape prevents the risk of rupturing of the pelvis, which risk is present in the case of prostheses with a frustoconical basic shape, when these are "drawn" too tightly upon screwing-in. On the other hand, the prosthesis with a hyperbola cross- section has a higher degree of stability to tipping and tilting than does the spherical cup. <IMAGE>