The problem of complex modeling of changes of material properties depending on physical and geometric nonlinearity for numerical simulation of the form-modification of thin-walled massive and combined axially symmetric bodies is considered. On the basis of classical papers, the basic concepts, the indifference of strain and stress tensors, and their increments under condition of energy compability are outlined in the description of the form-modification process. A large number of works are devoted to the problem of numerical simulation of the form-modification process of thin-walled massive and combined axially symmetric structures on the basis of FEM, but there are separately for each of the described classes of objects. It is narrows the scope of application of this development greatly. In this paper an attempt is made to construct universal mathematical models for description of the evolution of the stress-strained state of thin-walled massive and combined axially symmetric bodies, regardless of the type of the process of form-modification process. The indifference of the strain increment and the of stress increment tensor are shown, in which in both cases the same objective derivative is used. This makes it possible to use the taken measures to form the laws of the state of the material. The strain increment tensor are given as a product of the Aldroidi derivative on value of time increase, that allows for an additive decay similar to that adopted for the strain velocity and for their increments.