Finite element simulation of metal forming is based on the basic equations governing the physical process. The main constitutive equations describing the mechanical behaviour of metals are recalled, with usual friction laws modelling contact at the tool part interface, and the thermal coupling for hot forming. Different integral formulations are introduced which lead to various finite element discretisations and can be associated with several time integration schemes. Automatic remeshing is compulsory to model large strain which are usually produced by forming processes, and adaptive refinement must also be considered if one wishes to control the accuracy during the whole deformation. To reduce the computational time different methods are discussed, including: introduction of iterative solvers, use of parallel computers and adaptation of the multigrid method. Inverse methods are also investigated in the field of metal forming and their application to computer aided rheology and to process optimisation are analysed.

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