• The hysteresis and frequency dependency property are predicted by the proposed model. • The property of Gas pressure is evaluated by the ideal gas law with Energy Equation. • Considering fluid inertial combined with laminar flow model in connection pipes. • Significant effect of fluid inertial to the stiffness property of the HIS strut. • The model and experimental cover large working range of the HIS strut. Hysteresis properties exist in the Hydro-pneumatic interconnected suspension (HIS) system, which are mainly related to the gas state, inertial of hydraulic fluid in the long connection pipes and friction properties. The available model is normally simplified based on the ideal gas state equation and no hydraulic inertial assumption, and then cannot describe the dynamic properties of HIS strut accurately, which restricts the better application of HIS in different areas. In this study, the mathematical model of one kind of compact HIS strut integrating the gas chamber within the strut piston rod are proposed. The proposed model considers the gas state model described by ideal gas law with Energy Equation and the fluid inertial properties combined with laminar flow model across the connection pipes and seal frictions described by hyperbolic tangential hysteresis friction model, in which all the model parameters are identified through extensive experimental data. The validity of the proposed model has been verified through experimental under in-phase and out-of-phase harmonic excitations with different amplitudes and frequencies. The results show that the established model can not only describe the fundamental properties (force–displacement/velocity) with good accuracy, but predict the hysteresis phenomenon and frequency dependency property associated with both the gas pressure–displacement characteristic related to the heat transfer and the pressure-flow rate property between connection pipes related to the inertial of fluid flow reasonably well. The result also reveals that the effect of fluid inertial to the dynamic properties of the HIS strut is significant, which may make the stiffness performance worse under both in-phase and out-of-phase excitations especially high frequency excitation signals. [ABSTRACT FROM AUTHOR]