Methods of elastic solutions and interchangeable elasticity parameters for solving nonlinear boundary value problems of mechanics are considered, making it possible to describe non-isothermal processes of inelastic deformation with account of radiation swelling deformations and radiation creep of irradiated material. For modeling the processes of radiation swelling and radiation creep, modern approaches are used, which take into account the damaging dose, irradiation temperature, and the effect of the stress state on the material swelling and creep. Generalized and modified methods of elastic solutions and interchangeable elasticity parameters are investigated and applied to the solution of nonlinear boundary value problems of radiation creep. It is taken into account that the construction and investigation of the properties of iterative methods for solving the equations of radiation creep is complicated due to the fact that, in order to prove the convergence and estimate the accuracy of successive approximations, it is necessary to consider a rather rigid restriction due to the asymmetry of the operator, which relates the errors of the iteration process for two successive approximations. Under such conditions, traditional approaches to investigating the convergence of elastic solution methods and interchangeable elasticity parameters taking into account the properties of self-adjoint operators will prove to be unacceptable. In addition, the standard equation symmetrization procedure for successive approximations leads to excessively conservative estimates of the convergence of iterative processes, and therefore the optimization of their convergence rate has a rather approximate character. This problem is decoupled through a thorough study of the properties of the constitutive equations of radiation creep and the application of a special norm to the analysis of the convergence of successive approximations, which made it possible to construct modified iterative processes and prove the local convergence of elastic solution methods and interchangeable elasticity parameters for the general case of radiation creep equations. The properties of nonlinear operators of generalized and modified processes are studied in detail. On this basis, a priori estimates of the convergence rate of iterative methods for different models of compressed swelling are obtained. Using the obtained a priori estimates, optimization approaches for modified methods of elastic solutions and interchangeable elasticity parameters for solving nonlinear problems of radiation creep have been formulated.