A fast reduction of a reservoir level may result in instability of an earth dam caused by the high pore water pressures that remain relatively high in the embankment. Moreover, the dissipation of the accumulated pore water pressures is highly dependent on the permeability of the materials used for the embankment and the storage characteristics of the reservoir. Therefore, in the design of embankment dams, the stability analysis under rapid drawdown loading conditions is an important design case. In this study, the influence of different permeability rates on dam stability under different cases of rapid drawdownwas investigated using the finite element method in SEEP/W and SLOPE/W of the GeoStudio with a case of the Lugoda dam in Ndembera catchment, Tanzania. The modeling process considers the time-dependent hydraulic conditions and the transient flow conditions using different water levels during rapid drawdown for evaluation of the factor of safety. From the 1m per day drawdown rate; the lowest minimum factor of safety value (0.90) was obtained from the 10 -7 m/s material permeability of the upstream zone of the dam. It means that, at a drawdown rate of 1m per day, there is a potential for failure of the embankment if the hydraulic conductivity value will be somewhere below 10 -6 m/s.