Therefore in this paper we will present the stability analysis carried out on the Dwesat dam with vertical core, its high is 33m, the downstream slope of 1V:2.75H and the upstream slope of 1V:3.0H. Thickness of the vertical core was varied from 1V:0.25H to 1V:2.0H, and also present the effect of the varied thickness on slope stability for both upstream and downstream under three design conditions i.e. during and end of construction, steady state seepage and rapid draw down by General Limit Equilibrium Method using GeoStudio software. It was observed from the analysis that by varying the thickness of vertical core of earth dam, thinner core up to 1V:1.30H gives more stability and further increase in thickness of core tends to sharp decline in factor of safety for both upstream and downstream slope under different design conditions.