The objective is to investigate both steady and unsteady magnetohydrodynamic stokes flow of viscous fluid in the presence of magnetic force and the flow of fluid between parallel porous plate with an angular velocity by using analytical and numerical techniques. The work embodied in the present thesis is divided into eight chapters. The problems and the summary of the work done are presented below. This work deals with the introductory concepts and a survey of the literature. It analyzes the steady and unsteady magnetohydrodynamics Stokes flow of an electrically conducting viscous, incompressible fluid between two parallel porous plates of a channel with an angular velocity in the presence of a transverse magnetic field when the fluid is being withdrawn through both the walls of the channel at the same rate. An exact solution is obtained for all values of R (Suction Reynolds number) and M1 (Hartmann number with angular velocity). Expressions for the velocity components and the pressure distributions were obtained. The graphs of axial and radial velocity profiles have been drawn for different values of M1.