Creep properties of Beishan granite under temperature effect are investigated by using the MTS815 rock mechanics test system. A rheological element with thermo-damage coupling effects is proposed by considering the temperature effect coupled with the damage evolution during the whole creep stage. By replacing the Newtonian dashpot in the classical Nishihara model of the coupled thermo-damage element

a new creep constitutive model for full creep process under different temperatures is set up. Based on a series of creep tests carried out at different temperatures under uniaxial loading condition

the parameters of the creep constitutive model and the variation laws of them along with temperature are determined by fitting to the experimental results of the time-dependent deformation of Beishan granite. A sensitivity study for the analytic solution of the creep model with thermo-damage effect is carried out

showing the effects of creep parameters (including elastic modulus

viscosity coefficient etc.) on a creep strain of granite. In addition

a simplified formula of the creep constitutive relation in the case of no temperature variation and damage influence is given. It is shown that the new creep constitutive model can be simplified to the Nishihara model in the absence of temperature and damage effects. Comparison between the predictive results and experimental data，it is shown that the creep model proposed is capable to provide a precise description of full creep process in granite. In particular

the accelerated process is also well reproduced by the proposed model. A bigger exponent ? in the viscosity coefficient leads to a shorter steady-state creep process and earlier onset of the tertiary process.