In this study, a two-dimensional (2-D) heat transfer analysis was performed in circular and elliptic tube heat exchangers. The finite element method was used to discretize the fluid flow and heat transfer governing equations and a 2-D isoparametric, four-noded, linear element was implemented for the finite element analysis program, FEAP (O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, vol. 1, McGraw-Hill, London, 1989, Chapter 15). The numerical results for the equilateral triangle staggering configuration, obtained with the new element were then validated qualitatively by means of direct comparison to previously published experimental results for circular tubes heat exchangers (G. Stanescu, A.J. Fowler, A. Bejan, Int. J. Heat Mass Transfer 39 (2) (1996) 311-317). Next, a numerical geometric optimization was conducted to maximize the total heat transfer rate between the given volume and the given external flow both for circular and elliptic arrangements, for general staggering configurations. The results are reported for air in the range 300 less than or equal to Re-L less than or equal to 800, where L is the swept length of the fixed volume. Circular and elliptical arrangements with the same flow obstruction cross-sectional area were compared on the basis of maximum total heat transfer. The effect of ellipses eccentricity was also investigated. A relative heat transfer gain of up to 13% is observed in the optimal elliptical arrangement, as compared to the optimal circular one. The heat transfer gain, combined with the relative pressure drop reduction of up to 25% observed in previous studies (H. Brauer, Chem. Process Eng., August (1964) 451-460; S.N. Bordalo, F.E.M. Saboya, Determinacao experimental dos coeficientes de perda de carga em trocadores de calor de tubos circulares e elipticos aletados, in: Proceedings of the 13th COBEM, Congresso Brasileiro de Engenharia Mecanica (in Portuguese), Belo Horizonte, Brasil, 1995) show that the elliptical arrangement has the potential for a considerably better overall performance than the traditional circular one.