The influence of radiation on the unsteady free convection flow of a viscous incompressible fluid past a moving vertical plate with Newtonian heating is investigated theoretically. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. For a detailed analysis of the problem, three important cases of flow due to: (1) motion with uniform velocity, (2) uniformly accelerated motion and (3) exponentially accelerated motion of the plate have been considered. The dimensionless governing equations are solved analytically using the Laplace transform technique. Numerical results for the temperature, velocity, skin-friction and the Nusselt number are shown graphically. The results show that an increase in the radiation parameter leads to a decrease in the temperature and velocity. Also, an increase in the radiation parameter increases the skin friction and the Nusselt number at the plate. © 2011 Asian Network for Scientific Information.