A method and an apparatus determine the frequency or the period of the natural characteristic oscillation of a vehicle, and therefrom determine the mass of the vehicle and provide a warning if a dangerous oscillation condition exists which could lead to a tipping or rollover of the vehicle. The evaluation is carried out while the vehicle is driving. The apparatus includes a sensor such as a rotation rate sensor, a timer, an evaluating unit, and a warning unit. The method involves measuring the time interval between two characteristic features of the oscillation measured by the sensor, such as zero crossings, minimum points or maximum points of the angular velocity of the oscillation, and then calculating the period and/or the frequency of the oscillation from the measured time interval. Then the moment of inertia and/or the mass of the vehicle can be determined from the period or frequency. Also, if the period or frequency is out of a safe range, a warning is triggered to indicate to the driver of the vehicle that a rollover danger exists.