Long‐term mechanical property is critical for underground energy storage in a salt cavern. Multistage loading has been widely used in creep tests to save test time and cost. If the number of loading stages is too small or the loading time of each stage is short, the long‐term strength of salt rock is difficult to determine. For this reason, this paper carried out a ten‐stage loading creep test on the salt rock. The loading time of each stage is about 14 days, and the total creep time is more than 5 months. The stress‐strain curve and the stress‐steady‐state creep rate curve obtained from the test results can be well described by an exponential function. Based on the two‐stage power function model, a new method for determining the long‐term strength is proposed. The method is very similar to the results determined by the isochronous stress‐strain curve method. Moreover, considering that the rock is damaged during the accelerated creep phase, the stress will no longer be a constant value during the accelerated creep phase, but a slow loading process. In this paper, the accelerated creep phase is a coupled process of loading and creep. The total strain in the accelerated creep phase is equal to the sum of the loaded strain and the creep strain, and a new nonlinear creep damage constitutive equation is derived. The model was verified by the creep test results. The results show that the model can well describe the whole process of salt rock creep. It can theoretically explain the reason why the accelerated creep phase of salt rock exhibits nonlinear acceleration characteristics. Long‐term mechanical property is critical for underground energy storage in salt cavern. Multistage loading has been widely used in creep tests to save the test time and cost. If the number of loading stages is too small or the loading time of each stage is short, the long‐term strength of salt rock is difficult to determine. For this reason, this paper carried out a ten‐stage loading creep test on salt rock.