The applicability of catastrophe theory to research in higher education is considered, with several problems that typically appear in the literature presented in a theoretical framework. A catastrophe model is attempted for each. The nature of mathematical modeling and the relationship between modeling continuous systems and discontinuous systems are assessed. Characteristics that must be present in a system for it to be suitable for a catastrophe theory based model are bimodality, divergence, discontinuity or catastrophe, hysteresis, and inaccessibility. Attention is also directed to interpreting a catastrophe surface. Four issues pertaining to the use of catastrophe theory as a tool for modeling behavior in the social sciences are as follows: its foundations of the theory in mathematics and natural philosophy; the assumptions needed for its application; details surrounding specific applications; and the attitudes, style, and intellectual honesty of its advocates. Hypothetical examples for applying the theory are considered: faculty vitality as a function of promotion difficulty and percent of junior faculty hired, teacher expectations as a function of student communication and performance, and student attrition as a function of previous academic performance and educational aspirations. Based on the literature on catastrophe theory, it is suggested that the bridges between the theoretical applications and those actual applications where theory can be tested through quantification have begun to be built. It is concluded that the usefulness of the theory may come from the ability of its models to provide more complete, and possibly more precise, description than appears possible with theories describing continuous behavior. Additionally, graphs based on the theory provide good conceptual tools. A bibliography is appended. (SW)