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Abstract: Research on reservoir rock stress sensitivity has traditionally focused on unary granular structures, neglecting the binary nature of real reservoirs, especially tight reservoirs. Understanding the stress-sensitive behavior and mathematical characterization of binary granular media remains a challenging task. In this study, we conducted online-NMR experiments to investigate the permeability and porosity evolution as well as stress-sensitive control mechanisms in tight sandy conglomerate samples. The results revealed stress sensitivity coefficients between 0.042 and 0.098 and permeability damage rates ranging from 65.6% to 90.9%, with an average pore compression coefficient of 0.0168–0.0208?MPa?1. Pore-scale compression occurred in three stages: filling, compression, and compaction, with matrix pores playing a dominant role in pore compression. The stress sensitivity of binary granular media was found to be influenced by the support structure and particle properties. High stress sensitivity was associated with small fine particle size, high fines content, high uniformity coefficient of particle size, high plastic deformation, and low Young's modulus. Matrix-supported samples exhibited a high irreversible permeability damage rate (average?=?74.2%) and stress sensitivity coefficients (average?=?0.089), with pore spaces more slit-like. In contrast, grain-supported samples showed low stress sensitivity coefficients (average?=?0.021) at high stress stages. Based on the experiments, we developed a mathematical model for stress sensitivity in binary granular media, considering binary granular properties and nested interactions using Hertz contact deformation and Poiseuille theory. By describing the change in activity content of fines under stress, we characterized the non-stationary state of compressive deformation in the binary granular structure and classified the reservoir into three categories. The model was applied for production prediction using actual data from the Mahu reservoir in China, showing that the energy retention rates of support-dominated, fill-dominated, and matrix-controlled reservoirs should be higher than 70.1%, 88%, and 90.2%, respectively.