This paper presents an overview of the physical processes occurring during selective laser melting of metal powders, as well as a review of methods for mathematical simulation of these processes. The paper identifies the main physical processes that should be considered for adequate simulation of selective laser melting of metal powders. A general physical and mathematical model for solving the problem of selective laser melting of metal powders is proposed. It describes also the assumptions and restrictions for the considered physical model. Furthermore, it considers the initial equations describing the processes of heat transfer, liquid metal dynamics, and the shape of the free surface, along with the initial and boundary conditions. The numerical algorithm for solving the initial equations is based on a three-layer implicit scheme with second-order time integration accuracy, third-order counterflow approximation of convective terms, and second-order central difference approximation of diffusion terms. The pressure and velocity fields in the Navier-Stokes equations were coupled using the artificial compressibility method, modified for solving nonstationary problems. The system of initial equations was integrated numerically using the finite volume method. The numerical simulation of non-stationary processes of selective laser melting of metal powders provided a temperature distribution in the computational domain, including the indicating of the liquidus zone. The simulation enabled to determine the dependencies of the width and depth of the melt pool on the laser speed and the laser spot diameter.