Due to the immense applications of non-Newtonian fluids in engineering and industrial processes, they have received rising attention during the last several decades. Several constitutive equations have paved the path towards the classification of such fluids. The Williamson fluid model, which falls into the category of viscoelastic sheer thinning fluids, represents the behavior of pseudoplastic materials. It has been noticed that magneto hydro dynamic flow of an incompressible Williamson fluid past a porous plate has not been studied yet. Even this problem for a hydrodynamic case has not been analyzed. So the present attempt is made to investigate this problem. All the basic concepts and definitions have been detailed. As the resulting problem is a Non-linear one, the Homotopy Analysis Method (HAM), is employed to get an analytic solution. It is shown that how HAM works efficiently with its initial guess, linear operator and convergence control parameter to obtain a solution.