To study the effect of loading rate on the mechanical properties of salt rock, uniaxial compression tests and acoustic emission tests at different loading rates were carried out on salt rock specimens. The test results show that with increases in loading rate, the peak stress of salt rock increases first and then essentially remains unchanged, and the elastic modulus increases gradually, while the strain at peak stress decreases gradually. Moreover, the Poisson’s ratio is independent of loading rate. The macroscopic failure modes of the salt rock specimens at different loading rates are all ‘X’-type conjugate shear failure. However, the loading rate is closely related to the degree of fracture, such that the smaller the loading rate is, the higher is the degree of fracture of salt rock. In order to describe the stress–strain behaviour in the process of salt rock failure, a damage variable expression represented by the deformation modulus was proposed, and a rock damage constitutive model was established according to the theory of continuum damage mechanics. The rationality of the damage constitutive model was verified by using the present uniaxial compression test results of salt rock and existing test data from the literature. The results show that the model can accurately describe the stress–strain response of rock in the failure process.