Using two-dimensional Eulerian formulations coupling viscoplastic flow and heat transfer, the behaviors of aluminum alloys and stainless steel during FSW were overviewed. The plastic behaviors of the materials are complicated and the flow stresses are depending on deformation rate, temperature and deformation histories. Constitutive equations considering both strain hardening from accumulation of crystal defects and softening from recovery or recrystallization were used to model the materials. Strain hardening is incorporated with a strength that evolves with deformation rate and temperature along streamlines in the flow field. Strength evolutions have a Voce-like saturation limit because of the severe plastic deformation during FSW process. The model equations for kinematic and temperature were solved using the standard finite element method. The evolution equation for the strength is integrated along streamlines. The strength and temperature distribution vary with process conditions and constitutive equations. Stainless steel and AA6061 have different strengthening mechanisms. Modified constitutive equations were applied to reflect microstructural features of each material.