The purpose of this study is to suggest the methodology for the computation of uplift pressure and discharge of the seepage flow under gravity dam. A 3-dimensional FDM model is developed for this purpose and this model can simulate the saturated Darcian flow in heterogeneous media. For the verification of the numeric model, test simulation has been executed and the mass balance has been checked. The error does not exceed 3%. Using the developed model, The uplift pressure and seepage flow discharge under gravity dam has been calculated. The uplift pressure shows the similar pattern, comparing with the result of flow-net method. As the length of grout curtain increases, the uplift pressure decreases linearly, but the seepage flow discharge shows the non-linear decreasing pattern. The coefficients of the formulas in the dam-design criteria have been analysed, and ${alpha}=1/3$ corresponds to the value when the length of curtain grout is 70% of the aquifer height. The uplift pressure near the pressure relief drain has the big curvature vertically and horizontally. The developed model in this study can be used for the evaluation of the effects of seepage flow under gravity dam.