Two mathematical head-neck models have been developed using MADYMO:​ a global model and a detailed one. The global model comprises rigid head and vertebrae connected through nonlinear viscoelastic intervertebral joints representing the lumped behaviour of disc, ligaments, facet joints and muscles. The model response to frontal impacts agreed reasonably with volunteer responses. The detailed model comprises rigid head and vertebrae connected through linear viscoelastic discs, nonlinear viscoelastic ligaments, frictionless facet joints and contractile muscles. The model response to lateral impacts agreed excellently with volunteer responses, whereas the response to frontal impacts showed that the model was too flexible. The global model is especially suited for use in complex simulations as occupant behaviour in car crashes, whereas the detailed model is particularly suited for neck injury assessment.