Abstract: As the demand on the construction salt rock storage increases in China, the shallow suitable deposits have been gradually exhausted, as such, the utilization shift from shallow to deep salt deposits is an inevitable trend. In order to study the creep damage characteristics of surrounding rock under the coupling effect of three-dimensional in-situ stress and temperature during the actual operation of deep salt rock storage, the triaxial creep tests were carried out on deep salt rock specimens under different temperatures and stresses. Considering the influence of temperature and stress on the creep damage characteristic of deep salt rock, it is believed that the temperature damage is accompanied by the whole creep process, and the stress damage starts to play a role when the stress state reaches the yield limit. It is assumed that the damage variables relationship between temperature and stress satisfies Weibull distribution and negative exponential function respectively. A new viscoelastic-plastic creep damage model considering the temperature and stress coupling effect was proposed by introducing a fractional Abel dashpot to modify the Nishihara model. The proposed model not only has a simple form and clear physical meaning of parameters, which is convenient for the application of the model in numerical calculation and engineering practice. The results show that the steady-creep rate of deep salt rock is a function of deviatoric stress and temperature. The material parameter A= 32.39 MPa^−4.83/h, activation free energy Q=7.84×10⁴ kJ/mol and creep stress index n = 4.83 in the steady-state creep strain rate constitutive equation are fitted. The theoretical analytical solutions of the viscoelastic-plastic creep damage models under different temperatures and stresses are in good agreement with the corresponding experimental data, which verifies the correctness and accuracy of the model. The effects of temperature and stress on rock creep properties were verified by the fitting parameters of each mechanical body of the creep damage model, which proves the rationality of the established model. The theoretical model can not only accurately characterize the attenuation and steady-state creep stages of rocks, but also well describe the deformation characteristics of accelerated creep stages.