Abstract: Starting from the basic equations of the nonlinear theory of viscoelasticity,we deduce the successive boundary-value problems by the method of successive approximations. As a concrete example, we find the first-and second-order solutions for a thick-walled cylinder. On the inner surface of the cylinder, the displacement is prescribed, and on the outer surface, the traction is null. We thus obtain the formula in the second approximation for the stress field in the cylinder, Finally,we compare numerically the linear solution with the nonlinear one.

Key words: successive approximations, thick-walled cylinder, nonlinear viscoelasticity, boundary-value problems