A method of manufacturing a packing cup for a hyper-compressor is described. The method comprises the following steps: providing an inner disc (25), having opposed first front face (25X) and second front face (25Y), a central axial hole (18) and at least one lubrication-oil duct (23); autofrettaging the lubrication-oil duct (23); after autofrettaging, removing a thickness (D) of the inner disc on both faces thereof.