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The paper is concerned with the numerical solution of non-linear conservation laws, and the contribution biomechanical models of spine and of loaded wrist are formulated and analysed. The models are based on a contact problem in non-linear elastic rheology. The stress–strain relation is derived from a positive definite strain energy density function. For a weak solution of the problem, a variational inequality approach is used. Then the secant modules method and the finite element method are applied. First, the model of the weight bearing wrist, and secondly, the model of the Chance’s fracture of lumbar spine are discussed. [Copyright &y& Elsevier] more...