Theoretical analysis of unsteady magnetohydrodynamic free convection flow of a viscous incompressible radiative fluid past an infinite vertical plate with constant heat and mass flux is presented. The dimensionless governing linear partial differential equations have been solved using the Laplace transform technique. The exact solutions for the velocity, temperature and concentration fields are derived. The effects of radiation, magnetic field and buoyancy ratio parameters on the velocity and temperature fields are discussed through graphs. It is found that the velocity increases with increasing radiation parameter whereas it decreases with increasing magnetic field parameter for buoyancy assisted flows. © (2014) Trans Tech Publications, Switzerland.