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The effect of radiation on the flow over a stretching plate of an optically thin gray, viscous and incompressible fluid is studied. The fluid viscosity is assumed to vary as an inverse linear function of the temperature. The partial differential equations (PDEs) and their boundary conditions, describing the problem under consideration, are dimensionalized and the numerical solution is obtained by using the finite volume discretization methodology which is suitable for fluid mechanics applications. The numerical results for the velocity and temperature profiles are shown for different dimensionless parameters entering the problem under consideration, such as the temperature parameter, θr, the radiation parameter, S, and the Prandtl number, Pr. The numerical results indicate a strong influence of these parameters on the non-dimensional velocity and temperature profiles in the boundary layer.