Two methods of designing steel structures have been used in the United States during the past two decades as permitted by the American Institute of Steel Construction (AISC). These are Load and Resistance Factor Design (LRFD) and Allowable Stress Design (ASD). During this period of time the AISC published separate specifications and steel manuals for each method. In 2005, however, allowable stress design was changed to allowable strength design and combined with LRFD into one specification and one steel manual. The previous related studies are summarized and major related formulas are derived based on ASD (1989), LRFD (1999) and AISC (2005) specifications. Systematic arrangement is done on the beam-column related formulas and the limitations of these two design methods are specified. The basic difference of analysis among ASD (1989), LRFD (1999), and AISC (2005) are described. The limitation of axial force and moment interaction formulas of beam-columns is clarified. The study conducted some illustrated examples for description purpose, and numerical values are applied to demonstrate the calculation process in the beam-column analysis and design. The complicated procedure of calculation is computerized through the use of MATLAB so as to simplify the routine calculation and to make the analysis process faster and more convenient. The obtained analysis values from these two design methods are compared, and conclusions are made according to these two design methods, which are the ASD and LRFD as specified by the AISC.