Unified viscoplastic model hypothesizes material strain is divided into elastic part and viscoplastic part. Including stress part in its strain rate expression，that reflects the rock material characteristic of dependency of strength to loading rate, the characteristic of strain creep under continuous load and the characteristic of stress relaxation when with constant displacement. But showed the constitutive model of differential equations also result in difficulties in computation. Transformed the differential equations of constitutive model into integrated form, approximated the integrated form expressions by uniformly valid asymptotic expressions, and then the Newton-Raphson iteration pattern is established based on the approximate solution. A series of triaxial relaxation experiments is carrie out under different confining pressures, then based on the experiment data, a back analysis is made to get the parameters of the module. The results indicate that this model is able to describe the mechanical behavior characteristics of argillaceous siltstone under long-term loading.