It is suggested to use the path integration method for solving a number of problems of radiative kinetics of gaseous media. Temporal Green functions of integral equations of radiation trapping are represented in terms of path integrals. The classical Hamiltonian thus obtained makes it possible to develop the concept of an associated quasi-particle whose wave properties are described by the Biberman-Holstein equations. The problem on determination of all the effective radiative decay constants is reduced to the determination of quantized energy values of this quasi-particle locked in a gas cell. A formula for the calculation of the phase jump of the wave function of a quasi-particle upon its reflection from the cell walls is presented. The high accuracy (better than 3%) of quasi-classical methods (following from Bohr-Sommerfeld quantization rules) for the calculation of the complete spectrum of radiative constants is demonstrated by the example of a gaseous medium of a cylindrical configuration.