Hydro-pneumatic　suspension　models　built　on　the　ideal-gas　(IG)　state　equation　or　the　traditional　Benedict–Webb–Rubin　(BWR)　real-gas　(RG)　model　cannot　accurately　predict　the　variation　of　gas　pressure　during　suspension　movement　because　the　influence　of　gas　hysteresis　is　ignored.　This　leads　to　incorrectly　reflecting　the　properties　of　suspension　and　limiting　the　effect　of　control　methods　on　the　actual　suspension　system.　In　this　study,　the　RG　multivariate　index　model　considering　gas　hysteresis　is　identified　and　applied.　Based　on　this　model,　the　output　force　of　the　suspension　cylinder　is　deduced.　Then,　the　general　motion-force　models　of　full-vehicle　suspension　are　derived　by　applying　a　vector　method　based　on　a　six　suspension　cylinders’　test　platform.　Further,　the　stiffness　and　damping　property　formulas　under　different　working　conditions　are　discussed.　The　model＇s　accuracy　was　verified　through　sinusoidal　excitation　tests　on　a　full-vehicle　test　platform　under　different　frequencies　and　amplitudes.　The　maximum　discrepancy　of　gas　pressure　between　prediction　results　and　test　data　was　0.9%;　whereas　the　maximum　discrepancy　of　roll　moment　was　0.85%.　The　results　indicate　that　the　full-vehicle　suspension　models　can　accurately　reflect　the　influence　of　gas　hysteresis　on　the　performance　of　a　full-vehicle　suspension　system　and　be　applied　in　confidence.　©　2021　Elsevier　Ltd