Vehicle stability is a very important subject in vehicle design and control, because vehicle safety is closely dependent upon its dynamic stability. For the vehicle stability analysis, the nonlinear vehicle model of a mid-size car with three DOF - longitudinal, lateral and yaw - is employed. A rigorous method is used to determine the vehicle stability region in plane motion. An algorithm is used to materialize a topology theorem, which enables to find the exact stability region. A stability criterion for the critical cornering is proposed.