Abstract <p>Additive laser deposition technology is analyzed using the heat equation for a system containing an instantaneous concentrated heat source. The results demonstrate that, with some limitations, the fusion penetration depth in the substrate is described by a self-similar solution with sufficient accuracy. We have obtained two-parameter dependences of the fusion penetration depth and width on the Peclet number (ratio of the scanning speed to the rate of change in the temperature of the material) and dimensionless enthalpy (ratio of the specific energy absorbed by the material to the energy needed for melting) and found criteria for whether the knife fusion penetration or heat conduction regime will take place. The analytical relations we obtained have been shown to describe experimental data with sufficient accuracy.</p>