In this thesis an attempt is made to study the effects of Radiation and Magnetic field on unsteady free convection Heat and Mass transfer boundary layer flows past a vertical plate. In chapter 1 the effect of radiation on unsteady MHD free convection flow of a viscous incompressible fluid in presence of heat generation is studied. In chapter 2 thermal radiation and mass transfer effects on unsteady MHD flow of a viscous incompressible fluid past a vertical plate is considered. In chapter 3 the effects of thermal diffusion and radiation on unsteady hydromagnetic flow of a viscous incompressible fluid past a vertical plate has been studied. In chapter 4 unsteady hydromagnetic radiative flow of a viscous incompressible fluid past a vertical plate in presence of chemical reaction is investigated.In chapter 5 the effects of thermal radiation, time-dependent suction and chemical reaction on two-dimensional MHD free convective boussinesq fluid flow over a semi-infinite vertical plate in the presence of heat source is studied.