• Salt rock deformation under cyclic gas pressure is segmented into deceleration, steady-state, and acceleration stages.
• Cyclic gas pressure induces stepwise increases in axial and radial deformations, with radial deformation being more sensitive.
• A novel viscoplastic model incorporating cyclic gas pressure influence factor, axial loading influence factor, and state variable accurately predicts deformation.
• The state variable rate mirrors deformation stages and residual strain, reflecting internal hardening of salt rock.