At high operational speeds, the train system becomes very sensitive to parameter variations of components. Therefore, it is imperative to incorporate more accurate component models in the vehicle dynamics studies. This study addresses a more subtle and comprehensive non-linear parametric model of a highspeed rail hydraulic yaw damper. A new concept of a hydraulic yaw damper model is suggested, in which the small mounting clearance, the series stiffness, and the viscous damping are built in. The series stiffness is the tandem result of the dynamic oil stiffness, the rubber attachment stiffness, and the mounting seat stiffness. A dynamic oil property model is established and coupled to the entire modelling process, in which the density, the dynamic viscosity, the volumetric elastic modulus, and the stiffness of the oil are all changeable in terms of the instantaneous working pressure, the oil temperature, and the entrapped air ratio of the oil. The dynamic flow loss and the valve system dynamics are also incorporated. Experiments validated that the established non-linear parametric model is accurate and robust in predicting the damping characteristics within an extremely wide speed range. The validated damper model was then successfully applied to a thorough parameter sensitivity analysis and damping nature prediction under practical, in-service conditions. The established damper model couples all the main influential factors that are not or are insufficiently considered in normal-speed problems; thus, it will be more accurate and appropriate for furthering high-speed problem studies.Keywords Non-linear parametric modelling · Hydraulic yaw damper · Series clearance and stiffness · Parameter sensitivity analysis · High-speed train Nomenclature A e (m 2 ) equivalent action area on the valve seat B (N s/m) viscous damping coefficient of the piston-and-rod assemblydeviation rate of the relief valve F (N) damping force at a typical stroke speed F (t), F r (t) (N) nominal and initial instantaneous damping force H, H p (m) height of the inner tube and the piston K (N/m) spring stiffness of the relief valve 14 W.L. Wang et al.K e (N/m) series stiffness of the damper K leak (m 3 Pa −1 s −1 ) pressure leakage coefficient K oil (N/m) dynamic oil stiffness K q (Pa −1 s −1 ) flow coefficient of the relief valve K rubber (N/m) rubber attachment stiffness K seat (N/m) mounting seat stiffness L (m) piston seal width L gap (m) accumulated clearance at the ends of the damper L t (m) piston sweep distance P , P 0 (Pa) instantaneous and the reference working pressure P b (Pa) instantaneous back pressure P b0 (Pa) back pressure when piston is in the neutral position P t (Pa) set pressure of the relief valve Q (m 3 /s) instantaneous flow Q leak (m 3 /s) pressure leakage flow Q loss (m 3 /s) total flow loss Q valve (m 3 /s) flow forced through the complete valve system T , T 0 (°C ) instantaneous and the reference oil temperature V gas,0 (m 3 ) enclosed air volume when piston is in the neutral position V oil (m 3 ) instantaneous oil volu...