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A finite difference solution of an unsteady flow past an oscillating semi-infinite vertical place with variable temperature and uniform mass flux is presented here. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The dimensionless governing equations are solved by an efficient, more accurate, and unconditionally stable and fast converging implicit scheme. The steady state velocity, temperature and concentration profiles are shown graphically. The effect of velocity and temperature for different physical parameters such as the thermal radiation, Schmidt number, thermal Grashof number and mass Grashof number is studied. It is observed that the velocity decreases in the presence of thermal radiation. It is also observed that the time taken to reach a steady-state is more in the case of vertical plate than horizontal plate.