The aim of the present paper is to study the magneto hydrodynamic flow of conducting Walter’s visco-elastic fluid in a long uniform straight channel of rectangular cross-section under the influence of time varying pressure gradient and uniform magnetic field applied perpendicularly to the flow of fluid. The exact solution for the velocity of fluid has been obtained by using integral transform technique. Some particular cases of pressure gradient have been discussed in detail. Also we have discussed the case when magnetic field is withdrawn. Besides, the corresponding viscous flow problem has been derived as a limiting case when the relaxation time parameter tends to become zero.