The present study develops a new approach to minimize the weight of a radiating straight fin array so that the whole system of the fin array is optimized by minimizing the weight of the individual fin, which is subjected to radiation interaction with adjacent fins and base. The obtained system has the minimum weight possible, and also yields the best shape of the individual fins for a given total heat dissipation and uniform base temperature. Based on the present analysis, the optimum number of fins in a fin array is obtained.