The method of geometrical quantization for the specific conditions of the problems of radiation kinetics of gas media is developed. Integral reference equations are presented for the description of the spatial behavior of spectral modes of the equation of radiation trapping near the boundary of a gas cell, where the conditions of the quasi-classical approximation are violated. The explicit solutions of the reference equations are used to calculate the phases of scattering for an associated quasi-particle at the boundary of the cell, which are directly caused by the kinetics of the radiation transfer processes. The general criterion of applicability of the quasi-classical quantization rules is formulated. These rules are used to calculate the trapping factors for cylinders of finite length.