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In this research it is investigated the stability analysis of two-wheeled vehicles based on numerical definition of full range eigenvalues of a matrix linear approximation in the vicinity of the translation running. The received result was checked by numerical integration of an initial equations system of the disturbed running in that model. Inadequacy of two analyses is explained by specialty of considered mathematical model in which two parts in a complex conjugate eigenvalues close to each other that explains the emergence of standard derivations calculating their numerical definition. The model is asymptotically stable in the range wider than an operational interval (with 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce a design to the wheel vehicle additional resilient and damping elements between trucks and the case that will parry yaw mode of trucks.