An optimal unit sizing method for cogeneration systems is proposed using energy demands as continuous random variables. In this method, design variables such as equipment capacities and maximum contract utility demands are determined together with the systems' operational strategies so as to minimize an expected value of the annual total cost subject to the satisfaction of all the possible energy demands. In evaluating the expected value, decision variables and the objective function are considered as piece-wise linear functions of energy demands by applying a sensitivity analysis in linear programming and an enumeration method in mixed-integer programming. This optimization problem is formulated and solved based on a hierarchical optimization algorithm. A numerical study is carried out on a fuel cell cogeneration system installed in an office building. Through the study, the influence of uncertainties in energy demands on a system's economics and optimal equipment capacities are clarified.