Abstract: Triaxial creep tests of cores from the proposed underground salt-cavern storage were carried out and experimental curves for the whole process of muddy salt rocks creep were obtained. Based on nonlinear creep characters of the test and the damage mechanical theory as well as assisted with the Burgers model, we built a constitutive model for describing the accelerated creep stage of salt rocks. Furthermore, a method to distinguish parameters of the model was given and comparisons were made between theoretical data and experimental curves. The research result showed that a higher axial force in graded creep tests can speed up the destruction of the third creep stage (the accelerated creep stage). Both the initial strain value of accelerated creep and the strain value at creep rupture are decreasing with the increase of axial force, therefore, their behaviors are just opposite as the confining pressure increases. This constitutive model can well describe the whole process of salt rocks creep, which means the model are valid and rational.