Deformation stability plays a crucial role in the construction and operation of hydrocarbon storage salt caverns. Monitoring and analyzing wellhead pressure data under closed well conditions provide valuable insights into the evaluation of cavern stability. In this study, an analysis of five factors influencing internal brine pressure was conducted, which revealed that salt creep and brine thermal expansion contribute to an increase in internal brine pressure, while brine penetration, salt dissolution and cavern compressibility lead to a decrease. The atmospheric pressure, surface temperature, and earth tides are the other factors influencing wellhead pressure fluctuations. Through the analysis of wellhead pressure data from brine-filled salt cavern under closed conditions, the creep parameters of salt formations were calculated using the Norton-Hoff creep model. To further understand the behavior of brine-filled salt cavern, numerical simulations were conducted to analyze the brine temperature distribution and deformation stability. The volumetric average temperature of the brine exhibits a nonlinear increase over time, characterized by a rapid rise in the initial stage followed by a slower rate of change. Finally, the brine temperature stabilizes and converges toward the formation temperature. From deformation analysis, it was observed that the closed condition is more favorable for the maintenance of cavern stability in comparison to the open condition. The subsidence of the cavern roof is particularly sensitive and requires careful attention, especially for flat-roof salt caverns. Under closed conditions, it is crucial to control the brine pressure decrease rate and prevent excessively high brine pressure to ensure the mechanical and penetration stability of the brine-filled salt cavern. These findings provide valuable insights into the factors influencing internal brine pressure, the determination of creep parameters, the distribution of brine temperature, and the deformation stability of brine-filled salt caverns.