The production technologies development of thermonuclear reactors is a actual problem of today. The work researches zirconium goods used in the atomic industry – thin-walled tubes for the fuel elements shells, thin-walled tubes for the channels of watery and boiling reactors, rods for lock – plugs of fuel elements; mechanical properties of zirconium and zirconium alloys, production methods and technologies as well. The power approach is used in the work. The potential energy of the elastic deformation is regarded as a part of the plastic deformation energy and a portion of the energy used for residual stresses formation. Using these methods the distributions of residual stresses are determined by the volume of a product depending on the main technological parameters of a process and mechanical properties of the material. The results have shown that hoop stresses take maximum values. The activity of residual stresses can lead to the elastic deformations and to the departure from the rated dimensions of a product, subsequently, that is inadmissible for the precision parts. These methods are used to determine the influence of residual stresses on mechanical properties, precision and operating strength of tube products made of different zirconium alloys.