Numerical solutions for heat and mass transfer by laminar flow of a Newtonian, viscous, electrically conducting fluid on a continuously vertical permeable surface in the presence of a heat source, a first – order homogeneous chemical reaction and the mass flux are reported. The plate is assumed to move with a constant velocity in the direction of fluid flow. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The dimensionless governing equations for this investigation are solved numerically by Finite difference method. Graphical results for velocity, temperature and concentration profiles of both phases based on the numerical solutions are presented and discussed. Keywords: Chemical reaction, Unsteady, MHD, Heat and mass transfer, Vertical porous plate, Heat source, Finite difference method.