This paper deals with the unsteady Magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible viscous fluid past through porous medium between two parallel plates in the presence of a transverse magnetic field and Hall effect. An exact solution based on Laplace transform has been presented. For the numerical simulation of the problem we have employed the finite difference scheme. The effects of $M$ (Hartman number), $m$ (Hall parameter) and $K$ (Darcy parameter) on the primary velocity have been investigated and their profiles are shown graphically by using the Matlab software