A complex nonlinear rheological mechanical behavior of rocks is discussed。Based on Peirc’s Scale factor, a nonlinear elasto-viscoplastic constitutive model is proposed; meanwhile stress return algorithm and consistent tangent modulus are derived. According to the UMAT interface requirement of ABAQUS, the corresponding UMAT codes are programmed. The numerical test results show that the establishment of nonlinear elasto-viscoplastic rheological model can uniformly describe creep process under different stress states，which demonstrate the extensive adaptability of the model. Using the nonlinear elasto-viscoplastic constitutive model，the rheological numerical analysis is applied to rock tunnel, the variation with time of the tunnel crown settlement and contact pressure are obtained. These results indicate that the developed model is correct and reliable，and will have good application prospects.