Constructal theory introduces a new method to optimize the various engineering applications such as, extended surfaces fins. The aim of this study is to design and analyze a cylinder in which its heat transfer surface area is increased by fins using the concept of constructal theory proposed by Bejan. Three configurations including three branches, two branches and simple fins are presented. By the increase in the rate of heat transfer the volume of material applied in the fin should be increased. Therefore, the optimization is done by considering the total heat transfer rate and fin material as two objective functions. In order to maximize the heat transfer rate as well as minimize the volume of material five parameters are selected as the design parameters. The effects of decision variables on the rate of heat transfer for the optimum points are presented. In addition, the effect of increase in the number of fin branches on the heat transfer rate is estimated. Also fin temperature profiles for the three studied configurations for two cases of heat transfer rates are represented to indicate the effects of theory. Finally, the volume of material applied in the fin for two types of copper and aluminum in the fixed value of heat transfer rate is obtained for the different configurations, and the results are discussed.