Contains the papers presented at the third international meeting on the 'numerical analysis of weldability' organised by the International Institute of Welding and the Department of Materials Science and Welding at Graz University of Technology. The evolution in weld microstructure has been modelled using cellular automata, which enable non-trivial processes and patterns to be computed starting with simple deterministic rules. One paper describes a model which incorporates the effect of deformation on precipitation kinetics in the HAZ during welding of cold-worked aluminium. For the first time there is a detailed article on the precipitation of oxides from the liquid weld pool.