Abstract: In this paper, we presented the equations of the optimal strain paths for the nonlinear viscoelasticity and the viscoplasticity in one dimensional case. We also showed some character of the optimal paths,i.e(1)if the relation of the viscous part and the strain in the nonlinear viscoelastic constitutive equation is cave,the corresponding optimal strain path is cave;(2)the optimal paths of the overstress viscoplasticity and the Bodner-Parton one are that the plastic strain is linear and the plastic strain ra...