The finite element method is widely used in engineering applications to solve partial differential equations. The coupling of free flow with porous media flow has important applications in science and engineering. For example in geo-sciences in modelling the interaction between rivers and ground flow and in biological sciences in modelling blood flow. I will give a brief introduction to the finite element method and then present a numerical scheme to solve a coupled flow problem that models free flow using the Navier-Stokes equations and Darcy's law for the flow in the porous media. I will show existence and uniqueness results for both the weak and numerical solutions for the coupled flow problem. In addition, numerical results to illustrate the nature of the flow patterns generated and convergence of the numerical solution of the coupled flow problem will be presented.