The unsteady laminar flow of an incompressible, viscous, electrically conducting fluid in porous medium fully saturated with the liquid and bounded by torsionally oscillating disk in the presence of a transverse magnetic field has been computed. It is assumed that the flow between the disk and the porous medium is governed by Navier–Stokes equation and that in the porous medium by Brinkman equation. Flows in the two regions are matched at the interface by assuming that the velocity and stress components are continuous at it. Approximate solutions of the flow characteristics are obtained. Numerical results are presented graphically and discussed.