Abstract <p>This work reviews the numerical simulation of resonance radiation transfer in gaseous media with 3D geometry and under the conditions of nonstationary excitation and ionization kinetics. The rate balance equations for population densities of a multilevel atom are determined by direct and inverse collisional-radiative processes. At the same time, the probabilities of stimulated photoexcitation processes at any point of the gaseous medium depend on the radiation intensity averaged over solid angles and frequency. This average intensity is the sum of the external radiation intensity (which propagates through the medium and is absorbed by the atoms) and its own radiation formed by internal sources of photons. The mathematical formulation of the problem of collisional-radiative kinetics is given by a system of integro-differential equations. To calculate a triple integral over the frequency and angle variables, we apply discrete-difference methods, i.e., the method of discretization of the volume on impact planes. With developed unique techniques, methods, and computational algorithms, the Cauchy problem for a system of integro-differential equations is reduced to a system of ordinary differential equations, which is then solves numerically using the Adams and Gear methods. We provide the results for applying modeling in a certain class of problems of photoexitation and luminescence kinetics of gases under the action by external radiation. The research performed complements the astrophysical theory of radiative transfer and also makes a significant contribution to the development of spectroscopic methods for diagnosing radiating gases and plasmas.</p>