This paper gives very significant and up-to-date analytical and numerical results to the MHD flow version of the classical Rayleigh problem including Hall effect. An exact solution of the MHD flow of incompressible, electrically, conducting, viscous fluid past a uniformly accelerated and insulated infinite plate has been presented. Numerical values for the effects of the Hall parameter N and the Hartmann number M on the velocity components u and v are tabulated and their profiles are shown graphically. The numerical results show that the velocity component u increases with the increase of N and decreases with the increase of M. Whereas, the velocity component v increases with the increase of both M and N. These numerical results have shown to be in a good agreement with the analytical solution.