In order to study the stability of drainage culvert under overload dump, by taking a drainage culvert on flexible foundation of a mine dump as an example and considering the combined effect of vertical and lateral load limit states, a mechanical calculation model of box culvert was established, the axial force and shear stress of roof and side wall were calculated, its stability was evaluated, and the results were compared with numerical simulation and field investigation. The results show that the axial force on the left and right sides of the box culvert is the largest, and the shear stress and axial force on the chamfer of the box culvert are the largest. The numerical simulation results are in agreement with the calculation results. The overall stability of the culvert is good. The field investigation results verify the rationality of the mechanical calculation results. In the process of actual dump operation, it is strictly forbidden to pile up excessive soil in mines. This study provides important theoretical guidance for stability analysis of discharge culvert under dump.