Abstract: In this paper, the equivalence of two classical viscoelastic models for solids is proved and the shortcomings of these models are pointed out. The restrictions of thermodynamics upon parameters of the fractional exponential model¹ are given. It is shown by the comparison of calculations and experiments that since the model contains proper parameters, the model can simultaneously fit the experimental data of the creep and the relaxation processes of the same material with high accuracy by using the same set of parameters; the Stieltjes convolution of the creep compliance and the relaxation modulus of the model can equal the unit-step function approximately and in considerable wide frequency range the model can fit the storage modulus and the dissipation modulus very well. Since it has the advantage of high calculating speed and it can fit the experimental results of most real materials, the model can be widely used in the analysis of static or dynamic viscoelastic problems in engineering.