Natural convection heat transfer fluid flow past an inclined plate embedded in a fluid-saturated porous medium is investigated by Lie group analysis. The governing partial differential equations are reduced to a system of ordinary differential equations by the scaling symmetries. From numerical results, it is found that the thermal and momentum boundary layer thicknesses are increased as the radiation parameter is increased. Also, it is observed that the velocity is increased and the temperature is decreased for increasing the buoyancy parameter and the porosity parameter.