Salt caverns are widely used for energy storage. During gas storage, the internal gas pressure fluctuates cyclically in response to energy demand, making it essential to assess how these pressure variations affect rock deformation. In this study, experiments were conducted under different cyclic gas pressure conditions to investigate this effect. The findings indicate that (1) the deformation process of salt rock can be segmented into three stages: the deceleration stage, the steady-state stage, and the acceleration stage. (2) When the axial pressure remains constant, both axial and radial deformations exhibit a stepwise increasing trend in response to cyclic gas pressure variations. Similarly, under axial graded loading, the deformations also demonstrate a progressive rise. By analyzing the deformation differences and model coefficient fluctuations within a single gas pressure cycle, it is found that radial deformation is higher sensitive to changes in cyclic gas pressure. (3) The axial deformation shows a stepwise increase, and the radial deformation showed a cyclic change with changing gas pressure. Therefore, the cyclic gas pressure influence factor α, axial loading influence factor β, and state variable σ∗ are introduced to develop a viscoplastic ontological model that accounts for the impacts of cyclic gas pressure, confining pressure and axial stress. Validated by the deformation data, the new model can better fit both the axial deformation and the radial deformation of the three stages and has strong applicability and accuracy by changing only fewer parameters. The state variable rate shows the same stage as the deformation rate and residual strain of salt rock, which can better reflect the internal hardening of salt rock.