The thermal performance of rectangular plate fins circumscribing elliptic tubes is presented in this paper. Based on the assumption of uniform convective heat transfer the two-dimensional conduction equation has been formulated, and the solution has been obtained through the finite element method. Performance of rectangular plate fins for both inline and staggered arrangement of tubes has been investigated for a variation of geometric and thermo-geometric parameters. The necessity of optimizing the fin geometry for a given fin surface area has also been highlighted.