This work is to determine the optimum shape and minimum mass of a thin fin by incorporating the effect of radiative exchange between the fin and its base. Two types of the system are considered: a fin extending from a finite straight primary surface and a fin extending from a pipe. It is found that the predicted optimum shape and minimum profile area are governed by five important parameters, namely, the emissivity of the fin, εF, the emissivity of the base εB, fin base length, L̄ (or base pipe radius R̄), the environment temperature ξE and the heat flow from the base, γ. The present numerical results indicate that the radiative interaction at the base may affect the optimum shape and profile area of the fin significantly.