The application of solid mechanics theory in rock engineering is promoted by the presentation of sheet crack concept and geological model. The special part of rock mass with sheet crack is the problem of structural stability, the failure mechanism of which is different from the structural instability caused by material breakage. First, the rock mass slope with high-steep sheet crack is abstracted into an orthotropic plate to analyze its mechanical forms under different boundary conditions and obtain the non-dimensional buckling critical load of rock mass with sheet crack under different conditions of ratio between thickness and width in the elastic range. Second, the solution toward post-buckling mechanical behaviors of rock mass with sheet crack is processed to obtain the change rules of strength and bearing capacity after buckling, and the analytical solution for post-buckling critical load of rock mass with sheet crack is put forward, providing a new idea for stability analysis of slope and some theoretical reference for similar projects.