A nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Lie Group theory is applied to the equation. Group classification with respect to the thermal conductivity and heat transfer coefficient is performed. Results are summarized in a table for convenience. Some similarity transformations are used to convert the partial differential equation into an ordinary differential equation. (C) 2004 Elsevier Ltd. All rights reserved.