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The paper deals with the problem of vertical vibration of vehicles. The most commonly used theoretical vehicle models are presented, including examples of a simple full model (two-axle, chassis and a specific road vehicle model). Analytical and experimental solutions of the full model (considering only material friction) for a simple symmetrical model and a model considering some types of asymmetry are given. The time histories of the analytical solution of the simple model for some variables are given, as well as the results of the experimental solution (with the inclusion of material damping) and some results of the experimental solution of the railway car.