Using the examples of EB welding of a copper canister (for spent nuclear fuel storage) and multirun submerged arc welding of thick steel plates, the finite element (FE) methods (2D and 3D models) developed to simulate such industrial welding applications are examined. With respect to multirun welding, challenges imposed by addition of filler material, history dependency of the material and computer resources are considered. The FE developments discussed include combined shell and solid elements, adaptive meshing, techniques for extending the FE model, and computing phase changes/material properties for low alloy steels.