For a long time mathematicians have been developing a number of theorems that seek to establish general structural and behavioral characteristics of dynamic systems. Most of these techniques based on calculus have been designed for the study of continuous phenomena. Hence they are ineffective to deals with discontinuous or divergent behaviors. Catastrophe theory, when applied to scientific problems, deal with the properties of discontinuities directly without reference to any specific underlying mechanism. It is especially suited to the study of systems in which the only reliable observations are of the discontinuities. System dynamics, introduced by professor Jay W. Forrester in the early 1960's, is used to represent general, complex dynamic systems. It focuses on the structure and behavior of systems composed of interacting feedback loops. The nature of its approach to modeling shares many common points with catastrophe theory. Particularly, both are used to seek to develop fruitful simplifications of a complex reality. The purposes of this thesis, therefore, are: first, to offer a qualitative as well as a quantitative description of catastrophe theory, as this theory is not very familiar to many people; secondly, to present the relationship between catastrophe theory and system dynamics; and thirdly, to apply these theorem to urban transportation planning. / Master of Science