This paper proposes a formal structure for the study of insurance company capacity problems. Its first part develops the theoretical logic of this structure by applying a maximization (of profit) subject to constraints (on stability and survival) model to the risk selection and underwriting process. It is concluded that the stability constraint is generally the operative one and that capacity may be measured as a probabalistic distance from the constraint boundary. In the second part, this format is employed to explore hypothetical examples in catastrophe underwriting and to draw implications about the future of the capacity problem. Here it is shown that the present capacity shortage in the industry could be substantially alleviated by the increased participation of personal lines insurers in the industrial markets and that the shortage may be intensified by the current trend toward corporate self-insurance. In recent years, there has been much discussion in the insurance industry about something referred to as the "capacity problem." Loosely defined, the problem seems to be the inability or unwillingness of insurance underwriters to absorb the massive risks of modern industry. Concurrent with the discussions of insurance capacity, there has arisen a debate over the merits of the apparent trend toward self-insurance on the part of large corporations. There is general agreement among industry writers that a relationship between these two topics exists and that capacity shortages are partially responsible for the growth in self-insurance. James M. Stone, M.A., is Economist with Fairfield and Ellis (Boston). He is a Graduate Prize Fellow in Economics at Harvard University. Since 1969 he has been a Teaching Fellow in Economics, directing a number of undergraduate tutorial courses at Harvard. Mr. Stone founded Capital Dynamics Corporation in 1968 and serves as its President and as Chairman of Capidyne Systems Corporation. In his work with Fairfield and Ellis, Mr. Stone developed an analytical model for property and liability risk management in large corporations. This paper was submitted in May, 1972. The impact of self-insurance on capacity, however, does not appear to be clearly understood. The problem is that the concept of insurance capacity has never been clearly or precisely defined. Widespread misinterpretations of the nature of capacity have led people to a number of erroneous conclusions about the implications of self insurance and about the underwriting problems associated with catastrophe risks. The standard line of thought today seems to be that capacity is primarily determined by the amount of capital which an underwriter can commit to insuring a portfolio of risks. In this context, selfinsurance would be an unquestionably useful force in alleviating capacity shortages. The reluctance of underwriters to replace first dollar policies with catastrophe coverages would have to be ascribed to an appetite for investable cash flow or an irrational resistance to change. This article, in two parts, is designed to challenge the standard view of capacity and of the underwriting of catastrophe