Considering temperature dependent heat transfer coefficients and heat transfer from the fin tip, the optimum dimensions of rectangular fins and cylindrical pin fins are investigated analytically. In this work, the fin volume is fixed to obtain the aspect ratios of the uniform area cross-section fins with maximum heal transfer rates. The characteristic length thar has been determined empirically is taken into consideration in heat transfer coefficient. The analysis shows that an optimum aspect ratio of a fin is not found for a fin with heat transfer from the tip at a large fin volume or a large heat transfer coefficient at the fin base. However, there always exists an optimum aspect ratio for an insulated-tip fin. The optimum aspect ratio of a fin is highest for a fin with an insulated tip and decreases with increasing rate of hear transfer from the tip.