<p>The bedding structure in unconventional reservoir rocks, coupled with the unique properties of supercritical CO₂ (SC-CO₂), results in significant differences in fracture propagation behavior during SC-CO₂ fracturing in bedded rocks compared to water-based fracturing. However, due to the absence of reliable theoretical guidance for SC-CO₂ fracturing, the on-site application and promotion of SC-CO₂ fracturing technology have been substantially impeded. To address this issue, this study proposes a novel tensile failure criterion for bedded rocks, termed the “Y-L criterion", and verifies its accuracy by comparing it with existing criteria. By incorporating the effects of bedding structure and the fluid characteristics of SC-CO₂, a theoretical solution for the stress field at the wellbore wall during SC-CO₂ horizontal well fracturing in bedded rock was derived. Based on this theoretical solution and the proposed Y-L criterion, a fracture initiation criterion and a theoretical model for predicting fracture initiation pressure in SC-CO₂ fracturing were established. Experimental validation using SC-CO₂ fracturing on coal samples demonstrated that the error of the theoretical prediction model was less than 10%. Further research revealed that the horizontal in-situ stress difference was negatively correlated with fracture initiation pressure, whereas injection displacement was positively correlated with it. The influence of elastic modulus orthotropy is significantly greater than that of Poisson's ratio. Additionally, the bedding dip direction determines the orientation of the maximum effective tensile stress at the wellbore wall, while the dip angle primarily affects its magnitude. This research develops a theoretical foundation for advancing SC-CO₂ fracturing theory in unconventional reservoirs and provides theoretical guidance for the design and optimization of SC-CO₂ fracturing schemes.</p>