Abstract The creep shrinkage of a salt cavern with constant gas pressures was studied. The gas pressures have constant values, but their positions (i.e. cavern radii) change with time, which is negligible for small deformations rather than for large deformations. Based on whether the displacement of the cavern wall is considered in boundary conditions, small and large deformation solutions for cavern creep shrinkage were developed. To validate the solutions, the analytical results were compared with the numerical results. The results of the large deformation solutions showed good agreement with the numerical results in the case of small and large deformations. However, the small deformation solutions only applied when their results were sufficiently small; otherwise, the cavern shrinkage was overestimated. In addition, the sensitivity of cavern shrinkage to factors, such as time, creep parameters, and the difference between the geostatic pressure and gas pressure (pressure difference), was discussed. In some cases, the results of the large deformation solutions showed that the cavern shrinkage grows over time at a declining rate instead of a constant rate. For caverns of rock salt with great creep parameters, such as D and n in the Norton power law, the cavern shrinkage was fast. The cavern shrinkage rate decreased as the pressure difference decreased. The minimum internal pressure obtained by the large deformation solutions was lower than that obtained by the small deformation solutions, which can help to reduce the cushion gas in salt caverns. The large deformation solutions can provide useful references for gas storage in salt caverns.