ABSTRACT: This work presents a mathematical methodology for estimating the ensemble-averaged effective multiplication factor and the neutron scalar flux profile in statistically homogeneous, multiplying random media. The methodology is based on the generalized linear Boltzmann equation (GLBE), a neutral particle transport model that accounts for nonexponential neutron flux attenuation, which may arise in media where spatially correlated scattering centers occur. This nonexponential attenuation is incorporated through a carefully constructed free-path distribution function and a total macroscopic cross section, both of which depend on the neutron’s direction of motion and the distance traveled by the neutron since its last interaction (free-path variable). To solve the GLBE, we employ the spectral approach to handle the free-path independent variable, the discrete ordinates (SN) formulation to handle the angular variable, and the response matrix spectral nodal method to solve the resulting spectral SN approximation numerically. The conventional power method is used to estimate the effective multiplication factor. The numerical results to two test problems, associated with a one-dimensional, multigroup, random periodic medium, illustrate the methodology’s effectiveness in predicting the ensemble-averaged effective multiplication factor and the neutron scalar flux profile. These findings highlight the applicability of the proposed approach, particularly in cases where classical transport models may fail to provide accurate results due to their implicit assumption of exponential neutron flux attenuation.