Experiments show that the drilling deformation of rock is partly in the deformation stage of steady-state creep when the temperature is below 500 ℃ and the hydrostatic stress is below 150 MPa. In this paper, the generalized Kelvin model is selected to reflect its characteristics. By using the Laplace transform and the inverse Laplace transform, the analytical solution of the drilling's radial displacement is obtained, and the relationship between the model parameters, the temperature and the stress are obtained by taking the temperature-stress coupling effect into consideration. After applying the relation to a fitting calculation, it is shown that the model is rational and reliable and can represent the creep deformation characteristics of the granite in steady state and be used to obtain the creep parameters of the granite under high temperature and high pressure. The results can be used in the drilling construction and maintenance, the drilling deformation prediction, and the drilling shaft lining stability analysis during the development of hot dry rock geothermal energy resources.