To study the creep property of salt rock, uniaxial compression creep tests on salt rock specimens were carried out. The test results indicate that there is no steady creep of the salt rock used in this test in a strict sense. Even in the steady creep stage, the creep rate of salt rock changes continuously over time, but with a relatively smaller change range. When the axial stress does not exceed 9.5 MPa, the isochronous stress–strain curve of salt rock is approximately straight. While the axial stress exceeds 9.5 MPa, the isochronous stress–strain curve deflects to the strain axis, and the larger the axial stress, the more obvious the deflection. Thus, the long-term strength of the salt rock used in this test can be determined as 9.5 MPa. A mathematical expression for predicting the creep failure time of rock is proposed on the basis of assuming the change rule of rock strength over time conforms to the Usher function. Then starting from the variation in deformation modulus with respect to time in the creep process of salt rock, the elastic modulus of the damaged rock material is characterized by the deformation modulus, and the creep damage evolution equation of rock is established. Combined with the continuous damage mechanics theory, a new creep damage constitutive model for rock is proposed. The rationality of the model is verified using the uniaxial compression creep test results of salt rock. The results show that the new model can not only describe the attenuation and the steady creep of salt rock under low stress level, but also reflect the whole creep failure process under high stress level. The predicted curves under different axial stresses are all in good agreement with the test data.
