The aim of this paper is the modeling of a discharge produced by direct action laser-arc plasma torch (LAPT) of linear design, when the focused laser beam passes through the transferred arc along the axis of the plasma-forming channel. The mathematical model of the discharge in such plasma device was constructed on the basis of a system of magnetic-gas dynamic equations in the
boundary layer approximation for the plasma and a scalar wave equation in the quasi-optical approximation for the laser beam propagating in it. The results of the computer modeling have shown that for certain ratios of the arc current and the laser beam power the distributions of
temperature, current density and velocity of the plasma generated in LAPT differ basically from the corresponding distributions, which are characteristic of the arc plasma torches, while the laser beam is subjected to significant absorption and extra focusing in the plasma. The obtained theoretical results were used in designing of the torch for laser-plasma surfacing and selecting of its operation modes. The experimental examinations of LAPT have proved in general the results of its modeling.