Companies which design automation control for the metal rolling industry are faced with a growing demand for systems with higher performance standards than ever before. Along with these demanding specifications is always the problem of system stability at any given speed. A multi-ton rolling stand with uncontrolled oscillations not only destroys the product being rolled but may cause serious damage to the plant and endanger the lives of mill personnel. Therefore stability analysis is critical whether modeling individual mills or analyzing old products and strategies so as to invent better, cheaper control methods. Cost is another major consideration for the firm ordering these systems and the companies which design them. Suppliers are trimming time from design and production schedules wherever possible in order to compete in the world market. It is for these, and other reasons that computer aided stability analysis is so important. The object is to ensure a safe and stable system and yet minimize the time (and therefore cost) needed For design and installation. This paper describes a program (ROOT LOCUS) which was created to fill this need while using the tools and methods readily at hand. It was written for personal computers as these machines are rapidly proving to be cost effective solutions to problems in computing power. / Master of Science