We consider the axisymmetric problem of creep and creep damage for piecewise-homogeneous bodies of
revolution with meridional section of any shape. We develop a method for the solution of the nonlinear initial
boundary-value problem based on the combined application of the R -functions method and the Runge- Kutta-
Merson method. The structures of the solution for the main types of boundary conditions are constructed. We
present an example of calculation of creep, creep damage and long-term strength for a two-layer cylinder