Currently, numerous single-track railway lines are disused due to economic reasons. They could be reactivated by small vehicles that use only one rail and thus can be operated in both directions at the same time. MONOCABs are such small cabin-like vehicles, stabilized by a system of control moment gyroscopes and a trim mass. They could make an important contribution to improve the mobility offer especially in rural areas. Regarding the MONOCAB, there is currently no reference in comparison with other vehicles. In the context of mechanical design and construction, interdependencies with vertical stabilization occur. Torsional effects in particular can critically affect the stability. This paper investigates the influence of mechanical eigenmodes on the vertical stabilization system. Specific characteristics of the system (especially due to the gyroscopes) are highlighted by a model-based analysis. Moreover, a FEM modal analysis is used to examine the supporting frame of the vehicle. The results are compared to experimentally estimated frequency responses of a full-scale monorail vehicle.