<p>Fluctuations in gas pressure within salt cavern storage and the creep behavior of salt rock are key factors influencing the deformation of surrounding rock and the stability of salt caverns. Considering the operational characteristics of salt cavern storage, this study conducted triaxial graded loading creep tests on an impurity-containing salt rock to systematically analyze its creep deformation, strength characteristics, and failure modes under different confining pressures. The findings reveal that as axial stress increases, creep strain gradually becomes the dominant deformation component in an impurity-containing salt rock, while the proportion of instantaneous compressive strain decreases. When axial stress levels are similar, increasing confining pressure reduces both instantaneous compressive and steady-state creep strain rates. Under similar deviatoric stress conditions, a higher confining pressure leads to varying degrees of increase in instantaneous elastic strain, creep strain, and total strain of an impurity-containing salt rock. Under different confining pressures, the evolution of the steady-state creep strain rate and the viscosity coefficient follows an inverse function relationship. Based on the creep characteristics of salt rock and the geometric features of creep models in the nonaccelerated creep stage, a nonlinear integer-order viscous dashpot is proposed to describe the strain surge in the accelerated creep stage. A nonlinear viscoelastic-plastic creep model capable of capturing the entire creep process of salt rock is developed and further extended to a three-dimensional stress state. Comparative analysis demonstrates that the proposed creep model effectively describes the full creep process of different types of salt rock, particularly the accelerated creep stage.</p>