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The process of reducing a physical system to a mathematical representation is a prevalent task mutual to all fields of analysis. Sometimes the system of equations, or mathematical model as commonly known, will be modified on a trial and error basis to make the model respond in some predetermined fashion or react so as to match behavioral data obtained from the actual physical system. This paper presents a survey of activities to produce logically based schemes to generate mathematical models by making use of experimentally derived information. Primary attention is given to modeling of mechanical structures for purposes of dynamic analysis. Emphasis is given to current effort at Goddard and in particular to the recent studies designed to verify the practical effectiveness of a specific modeling scheme. Strengths and weaknesses of the various modeling schemes are discussed.