Flood forecasting can be predicted numerically by the solution of 1D (One-Dimensional) unsteady diffusive wave equation. This research paper presents the development of a fem (Finite Element Model) for flood routing using diffusive wave with and without lateral inflow/outflow. FEM is based on two-step semi?implicit Taylor?Galerkin technique. The accuracy of the model has been verified by comparing computed results with available solution of the diffusive wave problems available in open literature. Numerical results demonstrate that the technique is an efficient and accurate tool to simulate diffusive wave equation for outflow hydrograph for temporal variation of lateral inflow and outflow