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MADYMO is a computer program package for the simulation of two- or three-dimensional human body gross motions. Recently a two-dimensional airbag model has become available for MADYMO 2D. The airbag is represented in the model by a non-deformable ellipsoid or elliptical cylinder. Standard MADYMO features can be used in conjunction with the airbag model. This allows e.g. the simulation of belted occupants, inclusion of a separate sternum element in the thorax and connection of the airbag to a flexible steering column. Both driver and passenger side airbags can be simulated. The airbag contact algorithms have been validated on the basis of dynamical impact tests on an airtight driver bag, with various impactor shapes and impact velocities. In addition sled tests and full scale crash tests have been simulated. In this paper a description of the airbag model theory will be presented, particularly with respect to the penetration volume and contact force calculations.