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The finite element method was used in the current work to study the selection of the constitutive models, the selection of the frictional coefficients, the selection of the contact models and the selection of the physical parameters. Numerical results show that the shape of the shoulder can affect the material flows obviously and a total of about 54.3% energy can be transformed into heat in friction stir welding/friction stir processing (FSW/FSP). When the physical parameters are further considered to be functions of temperature, the predicted temperature is lower than the one in which the physical parameters are constant. When strainhardening effect is considered, the equivalent plastic strain is decreased and the corresponding energy dissipated by plastic deformation is decreased. The effect of the frictional coefficient on the prediction of the temperature field in FSW/FSP is small when the selection of the frictional coefficient is located in a reasonable small extent. The computational costs in the simulation of FSW/FSP are not only affected by the mesh sizes and wave speed but also affected by the mesh distortions. So, mesh distortions should be considered to be minimized in the numerical modeling of FSW/FSP to reduce the computational costs.