The ideas and methods behind a new system, ODESSY, for optimum mechanical engineering design are described. The motivation behind this work is found in the current trend toward unification of engineering design tools which were previously developed and used separately, namely geometric modeling in the form of CAD systems, and mechanical analysis in the form of finite element programs. The united capabilities of these techniques allow for a major step forward in Mechanical Engineering Design, i.e. from tools aimed at analysis to tools aimed directly at synthesis.