The Various Numerical Methods are applied to solve the spatially varied unsteady flow equations (Kinematic Wave) in predicting the discharge, depth and velocity in a river. Solutions of Kinematic Wave equations through finite difference method (Crank Nicolson) and finite element method are developed for this study. The computer program is also developed in Lahey ED Developer and for graphical representation Tecplot 7 software is used. Finally some problems are solved to understand the method.