The study presents preliminary results of theoretical analyses concerning interaction of quasi-cw laser radiation with an aluminium target. The range of laser power the authors were interested in was from 1 to 10 kW, and target thicknesses from 0.1 to 1 cm. It was also assumed that a laser beam diameter on the target (Al) was around 0.5 cm. A mathematicalphysical model of the phenomenon was based on the equation of conservation of energy (spatially one-dimensional model – (z,t)) taking into account: radiation absorption and transport inside the target, heat conduction, reflection of part of radiation from the target’s surface, and heat losses in the processes of melting and evaporation. Coefficients of light absorption and reflection from the target’s surface were described with semi-empirical expressions, which took into account their dependence on the temperature and density. Initially, a case of target static during heating was considered. Subsequently, the problem of enhancement of radiation interaction with the target (decrease of reflection coefficient) by the use of short (< 20 ns), high power pre-impulse was analyzed. The last case needed expansion of a set of equations with the continuity equation and the equation of motion, to take into account evaporation of target’s surface under influence of the pre-impulse. It was shown that thermal effect of the pre-impulse is practically not influencing final depths of target remelting. On the other hand, damage (matting) of the target’s surface by the pre-impulse, causing the decrease of reflection coefficient can have a substantial influence on the remelting depth.