The mathematical model is based on the physical and chemical mechanism of the fusion penetration of welded joints involving the energy of chemical interaction in a powder mixture in the self-propagating high-temperature synthesis (SHS) mode. The reacting mixture located inside the joint between thermal-conducting metal plates is initiated with a laser beam moving simultaneously along the plate contact boundary. The minimum power of the laser radiation and physical and chemical properties of the powder mixture needed to provide the sufficient velocity of the welding and depth of plate joint penetration have been determined. Numerical simulation has enabled to ground theoretically the possibility of realization of the SHS welding of both homogeneous and heterogeneous plates from aluminum and titanium with no steam-gas channel in the stable mode, when the intrinsic velocity of the SHS propagation does not exceed the welding velocity. (C) 2008 Elsevier Ltd. All rights reserved.