The article presents the results of the analysis of the plastic flow of titanium alloys in the process of the Linear Friction Welding (LFW). LFW is a high-tech process for joining critical structural elements of aerospace engineering from light and high-temperature alloys. Experimental studies of LFW modes of such alloys are expensive and technically difficult. Numerical simulation was carried out for understanding the physics of the LFW process and the formation laws of a strong welded joint of titanium alloys. Simulation by the SPH method was performed using the LS DYNA software package (ANSYS WB 15.2) and the developed module for the constitutive equation. The new coupled thermomechanical 3D model of LFW process for joining structural elements from alpha and alpha + beta titanium alloys was proposed. It was shown that the formation of a welded joint occurs in a complex and unsteady stress-strain state. In the near-surface layers of the bodies being welded, titanium alloys can be deformed in the mode of severe plastic deformation. A deviation of the symmetry plane of the plastic deformation zone from the initial position of the contact plane of the bodies being welded occurs during a process of LFW. Extrusion of material from the welded joint zone in the transverse direction with respect to the movement of bodies is caused by a pressure gradient and a decrease in the alloy flow stress due to heating. The hcp-bcc phase transition of titanium alloys upon heating in the LFW process necessitates an increase in the cyclic loading time to obtain a welded joint.