Abstract: There are not many analytical solutions for the viscoelastic material, and still less analytical solution for the viscoelastic material under nonconstant temperature state. In this paper, based on the 3-D constitutive equation 1 of thermoviscoelasticity under nonconstant temperature state, the equivalent relaxation curve of the material at terminal temperature state is expressed as the negative exponential function, and the analytic solution of the displacement is developed for the rod made of the vis...