Hydropneumatic springs are the elastic components of a vehicle’s suspension. As the nonlinear characteristic of the spring is difficult to express accurately, the statistical linearization method is introduced to analyze the dynamic response of the hydropneumatic spring. The nonlinear stiffness of a hydropneumatic spring is approximated by a quadratic polynomial at the static equilibrium position. Parameters of the hydropneumatic spring, road roughness and vehicle velocity are provided and analytical functions for equivalent stiffness and the dynamic equilibrium position are worked out in this paper. The analytical functions are validated through numerical simulation and are shown to be more accurate than those validated by existing methods. The method proposed here could be used in the design and analysis of hydropneumatic suspensions in future.