A numerical modeling technique is developed for the processes of coaxial laser gas-powder cladding occurring in additive technologies for the manufacture of complex geometry objects. The model is based on a three dimensional (3D) description of mutually related problems of gas dynamics, powder transport, laser heating, and thermal processes in the clad bead and substrate, which are considered without convection in the melt pool. The results of gas-disperse flow modeling with a triple coaxial nozzle are presented. Analysis of bead profiles on a flat substrate with variation in operating parameters is carried out. It is revealed that a self-consistent and practically reasonable model can be obtained when the considered processes are described in а mathematically conjugate 3D formulation. Comparison of the calculated bead profiles and experimental data (for the powder mixture with 16NCD13 steel and titanium carbide TiC) shows a good qualitative and quantitative correlation. In addition, regularities of the modeled repeated beam scanning and production of overlapped profiles of the beads lying beside each other on the flat substrate are discussed.