<p>This paper describes a numerical method for the linearization of the suspension forces of railway vehicles for the simulation of their ride on tracks with arbitrary geometry. The multibody formulation uses a kinematic description of the vehicle bodies with a combination of arc-length and track-relative coordinates. The suspension spring-dashpot components are assumed to apply forces that are linear in terms of their deformation and velocity of deformation. Therefore, the linearization performed in this work is only kinematic. It is shown that the suspension forces cannot be approximated as constant stiffness and damping matrices times the generalized coordinates and velocities, respectively, as it is common railway dynamics studies. This approximation is only valid in case of straight tracks. The general linearization of the suspension forces is achieved after the coordinate transformation into a new set that excludes the arc-length coordinates and includes the relative position and orientation of the track frames associated with the bodies connected by the suspension elements. With this procedure, the resulting stiffness and damping matrices, that are not constant but depend on the track design geometry, can be calculated online very efficiently. The validity of the linearization is demonstrated with the simulation of the ride of the vehicle defined in the Manchester Benchmark (Iwnicki in The Manchester Benchmarks for Rail Vehicle Simulation, Rail Technology Unit, Manchester Metropolitan University, Manchester, <CitationRef CitationID="CR1">1998</CitationRef>). Simulation results show that linearization of the suspension forces leads to a decrease of simulation time with a factor of 7. Comparison of the results with linear and non-linear suspension forces shows a good agreement in general. However, significant differences may appear when the vehicle runs of narrow curves.</p>