In this paper the problem of unsteady magnetohydrodynamic (MHD) flow of Oldroyd-B fluid flowing in a tube filled with porous medium is investigated. A uniform circular magnetic field is applied normal to the flow which is driven by an unsteady pressure gradient. The velocity field is determined for three cases; namely, the driving force is assumed to be axial pressure gradient which is either increasing or decreasing exponentially with time and the flow is induced by pulsating pressure gradient. The momentum equation and the equation of state that characterize the fluid are solved in exact manner considering the modified Darcy's law to account the resistance offered by the porous medium. The obtained velocity profiles possess Bessel and modified Bessel functions of zero order representations. The effects of the various pa-rameters on the flow characteristics such as non-Newtonian, magnetic and permeability parameters have been studied and discussed graphically. Illustrations are provided comparing the velocity profile for Newtonian, Maxwell and Oldroyd fluids. It is found that the velocity distribution increases with an increase of permeability parameter of the porous medium, while it decreases as the magnetic and frequency parameters are increase. The flow is basically parabolic for small frequencies while it possesses a boundary layer character at large frequencies. The solution for Maxwell fluids and Newtonian fluids appear as the limiting cases of the present analysis.