The purpose of this study is to develop a computer program to minimize the weight of steel frames using a penalty function technique. The program is developed and several example problems are analyzed. All structures are designed in accordance with the AISC code. One of the problems is also analyzed by the Fully Stressed Design method, and the penalty function solution has less weight, but takes more computer time. The penalty function solution is checked by hand and found to be a reasonable design. In this investigation, the penalty function method is found to be simple to use, reliable, versatile, and fairly economical for small structures. / Master of Science