The article deals with the problem of vertical vibration of wheeled vehicles. Due to vehicle asymmetry (both structural and load distribution asymmetry) and kinematic excitation asymmetry (due to road surface irregularities), the time course of wheel pressures is affected. This manifests itself not only in impaired driving stability, but also in increased wear on the wheels and the road surface (roads, railroad tracks). In extreme cases, the wheel loses contact with the track, which can cause the vehicle to become uncontrollable. The most commonly used theoretical vehicle models are listed, including examples of a simple complete model (two-axle railway bogie). As part of the work on addressing the impact of asymmetry on vertical vibration, a mathematical model was developed to predict vehicle behavior in critical situations where stability may be compromised, e.g., due to incorrect loading, structural asymmetry, asymmetric excitation, etc. A simple model was designed for analytical solution, which allows changing both symmetry (design and loading) and inducing asymmetric excitation. An analytical solution of a complete model with kinematic excitation for a simple symmetric model and a model considering certain types of asymmetry is presented. The time courses of deflections of the analytical solution of a simple model are given. An analytical solution for a more complex system is also outlined using the example of a railway wagon bogie with nine degrees of freedom.