Stability of soil slope in geotechnical engineering is one of the most important issues and since the earthquake is an essential factor in stability of soil slopes, assessment and dynamic analysis of soil slopes is always important. The homogeneous earth dams which prevent penetration of water by geomembrane are very suitable to store water and other liquids. Some dams do not need complex engineering calculations, their cost is low and they are not difficult to build. To ensure the geotechnical safety of dam, slopes embankments must be designed and built carefully. In this paper a number nomogram has been prepared in accordance with the geometry of the earth dams to calculate safety factor. The finite element method was used to calculate stability. The finite element method requires careful study of the mechanical properties of materials and calculating the stress and body displacement. ANSYS software modeling was used to model and examine the stability of the earth dam . To ensure the accuracy of the modeling and validation of the results, first the natural frequency of the system was studied using modal analysis and was compared with the results obtained from analytical relations. The results showed that the main contribution in improving the behavior of a reinforced earth slope is increasing the horizontal stiffness of the soil mass and the reinforcement significantly reduced vertical, horizontal, and shear strains. Also reinforcement reduced deformation of the slope outside surface. The amount of this deformation reduction depends on reinforcement spacing, slope angle, hardness of the soil and reinforcement, and foundation hardness. Generally use of reinforcements enhances the stability, protects the slope against coastal erosion, creates internal drainage in the dam and results in better performance. By increasing the height, the embankment reinforcement will consume the greater percentage of their resistance potential