Abstract: Gob area in open-pit mine directly influences safe production of operating personnel and large equipment. Based on Navier's solving method of rectangular thin plate with completed clamped supported, deflection equation and stress expressions under uniform load and concentrated load were derived separately, which turns out that the high stress under uniform load and concentrated load is mainly concentrated at the center of the plate and the midpoint of the long side. The factors that influence the stress are thickness, loading condition, dimension and Poisson ratio of the plate. In accordance with the first strength theory, the roof safety equations under uniform load and concentrated load were established, and the critical safety roof thickness was calculated. At last, the correctness of the equations was verified by engineering examples.