The major goal of the present work is finding the optimum cost design of frames as far as the materials as concrete, steel and framework are concerned using GAs method. Starting with the simplest parts of the frame as slabs, beams and columns with all its loading conditions, then designing plane frames and ending with the space frames under axial, flexural, shear and torsional loads. This is done by developing a computer programs (using MATLAB) with database to find the optimum sections in applicable dimensions, taking into consideration limiting the design results with the design constraints as much as possible. Checking the designed section capacities were carried out through a linear and non - linear reanalysis procedure to find out whether the optimum designed sections are capable of resisting the applied loads or not. Also, a parametric study was carried out through many examples to find out the factors affecting the optimum designed sections, such as concrete compressive strength, yield stress of steel and price ratio (steel price/concrete price).