Abstract: The paper studies the problem of a slope stability under the condition of before applying load and after applying load .The problem is analyzed and computed under the condition of applying cooling tower load by using finite element method and Mohr-Coulomb yielding criterion .From the result obtained we draw some conclusions: The stability of whole slope is mainly related to the deformation stability; The existence of columnar joint has adverse effect to the slope stability; The stability of slope is influenced by the cooling tower; The deformation of slope is enhanced with the growth of time; The main damage form of slope is toppling.