The stability of the upstream shell of the dams is changed under the rapid drawdown condition where the pore water pressure has a different values according to the soil permeability. This paper considers the stability of the upstream shell of the "Braddon" dam with many types of soil and analyses each type under two rapid drawdown programs, the first program is when the discharge happens, according to the irrigation outlet by 25 m3/s, and the second program is when the discharge happens according to the tunnel conversion of the river by 500 m3/s. The obtained results show, that the stability of the upper slope under considered boundary conditions changed according to the soil type. Some soil have good stability factor while other soil collapsed .Accordingly, we can conclude that the type of soil of the upper dam slope is important and we could chose the appropriate type which does not cause dangerous during the rapid drawdown. Also the study shows that: the highest values of the safety factors result when the slopes are formed of high permeability soils as well as the slopes of homogeneous soil, while the soils formed of materials between them appeared decreasing values of safety factors.