Additive technologies, in particular, wire-feed laser deposition, can significantly reduce the production cycle of manufacturing large-sized parts or parts of complex shape due to partial or complete elimination of technological operations such as casting, machining and welding. The aim of the work is to develop an analytical model of heating and melting of the filler wire during wire-feed laser deposition. The heat conduction problem was solved by the functional-analytical methods. The practical effectiveness of the functional-analytical methods with respect to computational time is several orders of magnitude higher than numerical ones. Obtained analytical solution made it possible to determine the temperature field for heat flux arbitrarily distributed on the filler wire surface. It is established that at a higher feed rate, the wire tip is completely melted at a greater distance from the laser axis. The shape of the melting surface also depends on the feed rate. At a slow feed rate, a more uniform heating of the wire over the cross section occurs. The melting surface has a small angle of inclination.
