We consider a mathematical model for accrual and costs associated with randomized clinical trials. A model that predicts the cost as a function of time can be constructed from the design assumptions of the trial and estimates of per patient costs of recruitment, treatment, and follow-up. Our notion of cost is a general one and includes personnel and paper flow as well as money. Costs associated with accrual and follow-up are distinguished in order to more accurately model per patient expenses. We assume that the investigator will specify these expenses in the same fashion that accrual and survival rates are estimated for statistical design. The size of the patient population to be followed can then be modeled and used to estimate cost. Although relatively simple cost equations result for the assumptions of constant accrual and exponential survival, very general assumptions can be incorporated into the model. The model has the advantages of predicting the time course of costs, allowing for different accrual and follow-up costs, and being amenable to revision during the conduct of a trial. Examples of cost modeling in a lung cancer clinical trial and cost minimization are offered.