摘要： The basic mathematical models, computational algorithms, and results of mathematical modeling of various modes of laser action on metals are considered. It is shown that for mathematical description and analysis of the processes of laser heating, melting, and evaporation of condensed media, various theoretical approaches are used: continuum, kinetic, atomistic, etc. Each of them has its own field of applicability, its advantages, and disadvantages. Mathematical description of ns-laser ablation is usually carried out within the framework of continuum approach in the form of hydrodynamic models that take into account reaction of irradiated material to varying density, pressure, and energy both in the target and in the vapor-gas medium. Within the framework of continuum approach, a multiphase, multifront hydrodynamic model and computational algorithm were constructed that were designed for modeling ns-PLA of metal targets embedded in gaseous media. It is shown that proposed model and computational algorithm allow to carry out the simulation of interrelated mechanisms of heterogeneous and homogeneous evaporation of metals manifested as a series of explosive boiling. Modeling has shown that explosive boiling in metals occurs due to the presence of a near-surface temperature maximum. It has been established that in ns-PLA, exposure regimes can be realized in which a phase explosion is the main mechanism of material removal. The verification of reliability of obtained results was carried out by comparing experimental data and calculations with atomistic models.