The study of steady two-dimensional incompressible magnetohydrodynamic (MHD) viscous fluid between two parallel porous plates is considered. The governing equations of the flow problem are reduced into nonlinear ordinary differential equation by using similarity transformations. The resulting equation of the problem is solved by using computer extended series (CES) and homotopy analysis method (HAM) with polynomial coefficients. The universal coefficients in the low Reynolds number perturbation expansion are generated. The analytic continuation of series solution unravel the flow structure which could not be fully revealed in earlier perturbation as well as numerical studies. The present analysis of the flow problem enables us to extend the study for higher Reynolds number R= 10 to 30. Both the solutions are found to be an excellent agreement and the results are demonstrated graphically.