ABSTRACT:  Reliance on low-fidelity models and assessments in nuclear reactor systems can result in overly conservative designs, unbalancing their competitiveness compared to other energy sources. Addressing this challenge toward developing the most economical designs and operation plans for existing and advanced reactor systems requires a comprehensive understanding of their behavior, effectively utilized in the design process. Consequently, computational modeling of nuclear reactors has garnered significant attention, leading to the development of phenomenological codes that can accurately capture key physics phenomena with medium to high fidelities. Efficient deployment of innovative nuclear reactors relies heavily on advanced modeling and simulation. This is particularly relevant in the context of Pebble Bed Reactors (PBR), which are considered one of the most promising solutions for the next generation of nuclear systems for energy production. These small-sized, modular reactors are inherently safe, efficient, and versatile, capable of generating electricity and providing heat for hydrogen conversion plants. However, designing PBRs presents a significant challenge due to the stochastic nature of their cores. The basic design of a PBR features a reactor core composed of a bed of spherical fuel elements (pebbles) consisting of thousands of fuel particles embedded in a graphite matrix. Hundreds of thousands are randomly packed in the reactor core, generating a sustained fission chain reaction, which is cooled by high-pressure gas forced through the interstitial spaces between the pebbles. Due to the dynamic nature of the reactor, the exact location of the spheres in the core is unknown, making this problem stochastic. Furthermore, the possible existence of correlations between the spheres (scatterer centers) inside the reactor may result in an attenuation of the particle flux that does not follow an exponential pattern, which is not considered by conventional mathematical models. Motivated by the concept of PBRs and the need to generate accurate results for complex neutral particle transport problems in multiplying media, we present a mathematical methodology to calculate the expected value for the system’s effective multiplication factor and the profile of the neutron scalar flux in statistically homogeneous random media. The methodology is based on a high-fidelity model called the Nonclassical Transport Equation (NTE), which expands the phase space of the transport problem to include the distance traveled by the particles since their last interaction with the background medium. This expansion allows the modeling of transport problems where the particle flux is not exponentially attenuated. The Response Matrix spectral nodal method is for the first time applied to solve the spectral approximation of the NTE, and the Power Iteration method is used to determine the system’s effective multiplication factor.