A 3D model of laser welding proposed before by the authors was extended to the case of welding of metallic plates made of dissimilar materials with a composite multilayer intermediate insert. The model simulates heat transfer in the welded plates and takes into account phase transitions. It was proposed to select the composition of several metals and dimensions of the insert to avoid the formation of brittle intermetallic phases in the weld joint negatively affecting its strength properties. The model accounts for key physical phenomena occurring during the complex process of laser welding. It is capable to calculate temperature regimes at each point of the plates. The model can be used to select the welding parameters reducing the risk of formation of intermetallic plates. It can forecast the dimensions and crystalline structure of the solidified melt. Based on the proposed model a numerical algorithm was constructed. Simulations were carried out for the welding of titanium and steel plates with a composite insert comprising four different metals: copper and niobium (intermediate plates) with steel and titanium (outer plates). The insert is produced by explosion welding. Temperature fields and the processes of melting, evaporation, and solidification were studied.