In order to study the influence of penetrating joints on the stability of tunnel surrounding rock, a finite element numerical model was established based on the strength reduction method, and the stability safety factors of tunnel surrounding rock were simulated and calculated under different conditions of joint dip angles, through-going positions, cohesion and internal friction angles. The quantitative relationship between the stability safety factors of tunnel surrounding rock and the sensitive influencing factors was analyzed. The results show that: (1) The dip angle of joints passing through the tunnel center has a relatively small impact on the stability of the surrounding rock in the bare tunnel, and joints passing through the arch foot have a more significant influence. As the dip angle of the penetrating joints increases, the stability safety factor of the tunnel surrounding rock gradually decreases. (2) As the penetrating joints move from the bottom to the top of the tunnel, the stability safety factor of the surrounding rock first increases and then decreases. The stability safety factor is the highest when the joints pass through the tunnel center, and it decreases as the through-going position approaches the excavation boundary of the tunnel. There is a greater impact on the surrounding rock stability when joints pass through the lower half of the tunnel than those passing through the upper half. (3) As the cohesion and internal friction angle of the joint surface increase, the stability safety factor of the tunnel surrounding rock gradually increases, and greater sensitivity to changes in the internal friction angle. (4) The main prevention and control measures for joints passing through the tunnel were summarized. The research findings can provide references for the design and construction of tunnels in areas with well-developed joints.