Z. Barikbin - Department of Mathematics, Imam Khomeini International University, Ghazvin, ۳۴۱۴۹, Iran
R. Ellahi - Department of Mathematics & Statistics, Faculty of Basic and Applied Sciences, International Islamic University, Islamabad, Pakistan
S. Abbasbandy - Department of Mathematics, Imam Khomeini International University, Ghazvin, ۳۴۱۴۹, Iran

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution of algebraic equations.