On the basis of rock failure process analysis（RFPA）code

together with the time-dependence of the rock progressive damage and the creep constitutive relation of the characteristic elements at a mesoscopic scale

the rheological model of rock in the failure process under loading is further developed. Using the further developed RFPA code

the progressive creep failure of rock specimens under constant loading was numerically simulated and the typical time-dependent deformations: the transient creep

the steady-state creep and the accelerating creep were also represented. The fact that the simulations are well tallied with the observations in laboratory shows that the rheological model is appropriate to investigate the nonlinear complicated creep failure of rocks. The numerical simulations indicate that the macroscopic creep failure is induced by clusters of microfracturing at a meso scale. The above numerical results offer us some important theoretical indications and practical instructions to further investigate the instability failure mechanisms of engineering rockmass and take some precautions to prevent their occurrences of rock hazards in rock engineering.