The paper carries out research into elastoplastic unloading using methods of plasticity theory and solid mechanics. Residual stresses are measured in a heavy-walled tube made from a dispersion-hardened copper alloy. It is shown that residual radial stresses are insignificant after the unloading and do not exceed 0.5 MPa. When the ultimate plastic strength is achieved, the amount of residual tangential and axial stresses is almost 17% of the ultimate shear stress.