Results of mathematical and numerical simulations of linear friction welding (LFW) process are presented. A mathematical model of heat generation due to the nonlinear process of friction is formed as well, as different models of pressure distribution in contact area are developed. It is illustrated, that nonuniform distribution of contact pressure causes nonlinear temperature development in the contact area. The shape of the temperature profile depends on material properties. The effect of applied forces geometry is investigated using developed model. Comparison of the mathematical modeling and numerical simulation using ANSYS software is performed when good qualitative agreement is obtained. A numerical model of the equilibrium stage of LFW process, using the FE software, is developed. In order to avoid difficulties with simulation of large plastic deformations the stepwise method of a simulation of the shortening process during the LFW with visualization is developed.