Vehicle mass is a crucial factor for the distribution of injuries between occupants in involved vehicles in a two-vehicle crash. A larger vehicle mass protects the occupants in the vehicle while on the same time inflicts a higher injury risk on the occupants in the collision partner. This mass externality can be internalized to reach a situation where the drivers choose vehicle mass based on the social optimum instead of a private optimum that ignores the negative effects that a large vehicle mass has on the injury risk in presumptive collision partners. Using a database including collision accidents in Sweden involving two passenger cars during five years, the influence of vehicle mass on the injuries and thereby the accident cost in both vehicles is explored. The database contains information on road infrastructure, vehicle characteristics including vehicle mass and characteristics of the occupants in the vehicles including their injuries. To get a measure of the accident cost the Swedish official economic valuation of slight injuries, severe injuries and fatalities are applied. In each accident the two involved vehicles are divided into the lighter vehicle and the heavier vehicle and the effect of weight is examined separately for the two groups. The accident cost that falls on the lighter vehicle increases with the mass of the heavier vehicle and decreases with own mass. Given that a vehicle is the heavier one in the crash, neither the own mass nor the mass of the lighter vehicle significantly affect the accident cost. The expected external accident cost is calculated and it is shown to increase rapidly with vehicle mass. The paper discusses different solutions to internalize this external accident cost and calculates a mass dependent multiplicative tax on the insurance premium in a no-fault insurance system.