O - ABSTRACTOur knowledge of vehicle behaviour and road safety systems was based at INRETS (Institut National de Recherche sur les Transports et leur Sécurité - National Research Institute on Transport and their Safety) on impact tests. A program was initiated on the modelling of the front compartment of a vehicle in the case of barrier impact tests. The model should allow us to enlarge the conclusion drawn from test results by extending the studies to different crash-test configurations.One dimensional lumped-mass model has been used for several years to simulate structural collapse in tests. The present paper describes tools which have been developed in order to use two or three dimensional lumped-mass models (in particular to study asymmetrical barrier impacts).Usually the methods used for the formation of equations governing the movement of a complex system are based either on the use of general theorems or on the use of techniques of analytical mechanics (Lagrange's and Hamilton's equations). Our idea is to start from a method allowing us to draft these equations in a more synthetical form in order to leave most equation developments at the computer level (by using symbolic calculus). Because of its differentiable properties, the displacement group is a LIE group. We use them for calculations. The final advantage of this type of method is that it allows a totally intrinsic analytical calculation in the vectorial space of torques or equiprojective fields.