In this paper we discuss an analytical solution of unsteady MHD flow between two parallel plates through a porous medium with uniform suction in the lower plate and uniform injection in the upper plate. External uniform magnetic field are applied perpendicularly to the plates while the fluid motion is subjected to an exponential axial and transverse velocity and pressure gradient. The solution of the problem is obtained with the help of similarity transformation. The exact solution of the velocity in the porous medium is analytically derived, its behaviour computationally discussed with reference to the various governing parameters. The axial and transverse velocity of the fluid and the pressure distribution are presented. Analytical expression is given for the velocity field of the fluid and the effects of the various parameters entering into the problem are discussed with the help of graphs.