Abstract: On the basis of elasto-viscoplastic theory of Perzyna,a mesoscopic coupled elasto-viscoplastic damage mod-el,describing the whole creep process of rock from initial creep,stable creep to nonlinear acceleration creep,is con-structed by introducing a mesoscopic unit strength damage model based on the strain energy theory. The characteristics of the creep rate change with time in the creep process of rock can be taken into consideration,and can be integrated into the EPCA3D . The model was verified by the experimental data and then applied to the numerical experiments of single and triaxial compression creep process under different axial stresses,confining the pressures and homogeneity coefficients. The results showed that,on one hand,the increased axial stress can speed up the creep rate,which reduces the creep failure time. On the other hand,the increased confining pressure and homogeneity coefficient can re-duce the creep rate and lead to the increase of creep failure time. This study can better reproduce the typical experi-mental phenomena. It can be used to explain the mechanical mechanism of creep-induced rock burst in coal mines, and also better reflect the accumulation of elastic strain energy after the excavation of coal mine roadway and the dam-age process of surrounding rock undergoing stable creep and accelerating creep. This study can provide an analytical tool for the long-term stability of rock mass engineering.