Abstract— A numerical study of unsteady MHD pulsating flow of an incompressible Newtonian electrically conducting couple stress fluid through porous medium between permeable beds under the influence of periodic body acceleration. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of Navier-Stokes and that in the permeable regions by Darcy's law. The slip condition plays an important role in shear skin, spurt, and hysteresis effects. The fluids that exhibit boundary slip have important technological applications such as in polishing valves of artificial heart and internal cavities. A numerical solution of the equation of motion is obtained by a new algorithm "modified generalized differential quadrature method (MGDQM)" which applying a generalized differential quadrature method (GDQM), to derivatives with respect to space variables of differential equations and for the time derivative applying 4th order Runge Kutta Method. This combination of DQM and 4th order RK method gives very good numerical technique for solving time dependent problems. The numerical results and the effects of the material parameters are presented and discussed through graphs.