This study analyzes and optimizes a design for a convective and radiating annular fin of rectangular profile using the two-dimensional analytical method with the radiation effect being linearized. The analytical solution for the temperature along the fin height at the fin tip is presented to show the two-dimensional effect. The heat transfer, fin length, and fin height with various radiating characteristic numbers are optimized as a function of the convection characteristic number, the overall wall resistance, the ratio of convection from fin surface to tip and the dimensionless fin volume. Corresponding to the optimum conditions, the fin effectiveness is calculated which is shown as a function of the convection characteristic number and radiati on characteristic number.