The article presents the mechanism studies results for changing the precision parts dimensional accuracy such as bearing rings, arising from the residual stress diagrams asymmetry relative to the rings transverse and longitudinal sections main axes occurring during the relaxation process. The stabilizing geometric parameters’ problem is especially acute in the accuracy’ precision rolling bearings production classes 6 and higher, which are widely used in various machines and units. Even a slight change in dimensions over a time certain period leads to an accuracy sharp loss in these bearings. The existing technology and known methods for stabilizing geometric parameters, such as heat treatment, low-temperature tempering, artificial ageing, are ineffective since their use in practice lead to high energy costs, and the geometric dimensions and shape refinement degree is negligible. Therefore, work on improving the technology for stabilizing the precision bearings geometric indicators is very relevant.