<p>A biaxial compressive strength prediction model for vertically intersecting double-hole samples was proposed in this paper. Firstly, by incorporating the intermediate principal stress<i> σ</i>₂ into the conventional Mohr-Coulomb strength criterion, a formula for calculating the biaxial compression strength of intact rock was derived. Then, the hole reduction coefficient <i>K</i>_<i>hole</i> was introduced to account for the effects of hole spacing and penetration on rock strength, proposing a hole reduction model. Finally, a prediction model for the biaxial compression strength of vertically intersecting double-hole samples was finally proposed, which was validated against experimental results. This model explicitly quantifies the coupled effect of two coexisting holes and their geometric configuration on the macroscopic strength of rocks by introducing the hole reduction coefficient. It overcomes the technical shortcomings of existing biaxial compression strength prediction models of rocks, which fail to accurately reflect the strength-reducing effect of double hole interaction. Compared to complex full three-dimensional numerical simulation methods, this model offers a simpler and more efficient computational process. Furthermore, the computational process of this model is simple and efficient.</p>