An idealization of the elastic compression of the car on the basis of representing the car-body as a cylindrical shell with elastic wrinkles shows that three main factors govern the rebound velocity and hence the coefficient of restitution. These are the 3/2 power of acceleration at maximum dynamic crush, the square of the ratio of car-body mass to overall car mass and the half power of the position of the plastic/elastic crush interface. The model is applied to predict mean rebound characteristics for the car population. A comparison with published experimental data of the coefficient of restitution of the car population in frontal impacts with rigid barriers at impact speeds up to 100 km/h was made. The model predicted values of e similar in magnitude to those of the car population and also predicted a similar reduction in e with increasing impact speed.