Collapse is one of the most significant geological hazards in mountain tunnel construction, and it is crucial to accurately predict the collapse probability. By introducing the reliability theory, this paper proposes a calculation method for the collapse probability in mountain tunnel construction based on numerical simulation, support vector regression (SVR), and the Monte Carlo (MC) method. Taking the Jinzhupa Tunnel Project in Fujian Province as a case study, three-dimensional models were constructed, and the safety factors of the surrounding rock were determined using the strength reduction method. By defining the shear strength parameters of the surrounding rock as random variables, the problem was formulated as a reliability model, and the safety factor was chosen as the reliability index. To increase computational efficiency, the SVR model was trained to replace numerical simulations, and the MC method was adopted to calculate the probability of collapse. The results showed that the cause of the collapse was the change in the excavation method and the very late installation of supports. The feasibility and reliability of the proposed method have been verified, indicating that the method can be used to predict the probability of collapse in a practical risk assessment of mountain tunnel construction.