The paper describes the theoretical simulation of roll over accidents. A brief account of the findings of accident investigation into bus roll overs is given. This shows that most actual rolls occur with lateral vehicle motion. The simulation starts with a vehicle dynamics program which reconstructs manoeuvres necessary to initiate lateral motion. After impacting a ‘kerb’ the free body roll motion is simulated until the structure impacts the ground plane. When the roof structure impacts the ground a structural collapse program (CRASHD) is used to obtain the deformation history of the vehicle structure. The dynamic program allows for energy absorption by the ground and vehicle structure and simulates further rolling motion and impacts with structural collapse where appropriate. The vehicle may be rolling on level ground, down a slope, or falling from an elevated highway. As experience is gained on the modelling of structural collapse in other types of vehicle structures, it is believed that the program will enable certain accidents to be simulated theoretically.