Аннотация:An exact analytical solution to the problem of large deformations of a multilayer cylindrical rod under multistage deformation is obtained for incompressible isotropic nonlinear elastic materials. At each step of deformation, another layer is attached to the rod, after which twisting and tension–compression of the cylinder along with the attached layer occur. The solution is obtained on the basis of the theory of multiple superposition of large deformations using one of the universal solutions of the problem of nonlinear elasticity. Numerical results are given. Nonlinear effects and effects associated with superposition of large deformations are analyzed.