The aim of this study is that optimum solutions and seismic responses are compared between minimum weight and minimum cost steel frames. The minimum weight problem to minimize structural weight under constraints based on Japanese seismic code and the minimum cost problem to minimize sum of steel material cost and fabrication cost are formulated and solved by genetic algorithm. The adaptability to practical use is discussed for each frame. Moreover, time history analyses are performed and the difference of seismic responses between inner beams and outer beams are discussed for each frame.