Two new correspondence principles, which are called elasticity recovery correspondence principles, for problems involving a class of nonlinear (or linear) viscoelastic materials in one-dimensional case are proposed in this paper. By means of these principles, solutions to nonlinear viscoelastic problems can be obtained as long as the solutions to the corresponding nonlinear elastic problems exist. The idea of these principles is entirely different from the traditional one. Not the similarity between the elastic constitutive relation and the viscoelastic relation is utilized. Rather, the recoverability from the nonlinear viscoelastic response to the nonlinear instantaneous elastic response is utilized. It is shown by experiments for modified polypropylene that these principles are applicable for such a class of materials.