The unsteady free convection flow past an infinite vertical plate with Newtonian heating has been studied in the presence of thermal radiation for a uniformly accelerated plate and an exponentially accelerated plate. The problem is solved under the conditions of (i) uniform wall concentration (UWC) and (ii) uniform mass flux (UMF) by Laplace transform technique. Closed form analytical expressions for the velocity and the skin-friction are obtained for various cases. It is observed that an increase in the buoyancy ratio parameter leads to a decrease in the skin-friction. © 2012 American Institute of Physics.