Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical Surface ill presence of thermal radiation is considered. Fluid viscosity is assumed to Vary LIS a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order Coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid Viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease. (C) 2007 Elsevier Ltd. All rights reserved.