The aim of the article is to form the concept of technology for determining the permeability and porosity properties of terrigenous reservoirs using mathematical modeling methods on a digital rock sample model. Digital rock sample modeling is used to assess geological oil reserves. The article presents the concept of digital rock sample modeling technology, which allows carrying out qualitative investigations to determine the permeability and porosity characteristics of the formation, including modeling the pore space and filtration processes. The essence of the concept is that the simulation model of the microstructure for the digital model is formed on the basis of a large number of parameters obtained during lithological and petrographic investigations of thin sections, a study of the sludge and geophysical investigations of wells. The acquired model can be used as a basis for subsequent modeling of filtration processes. Conductivity of single channels of the formed model can be calculated using molecular dynamics methods, models of Boltzmann's lattice equations, and other mathematical models and methods. Based on the results of the study carried out, the application of stochastic packing methods for modeling the structure of the pore space in the digital rock sample model of terrigenous reservoirs is substantiated. In connection with the development of computer and nanotechnologies and their use in the oil and gas industry, solutions that allow obtaining adequate results of digital rock sample models are of high importance and relevance for the production sector. It is especially important to use digital rock sample models in the study of reservoir rocks of shelf fields in the western part of the Russian Arctic, oil shales, rocks represented by loose weakly cemented reservoirs, and others, which are complex for physical experiments.