The design of mineral processing circuits is a complex, open-ended process.  While several tools and methodologies are available, extensive data collection accompanied with trial-and-error simulation are often the predominant technical measures utilized throughout the process.  Unfortunately, this approach often produces sub-optimal solutions, while squandering time and financial resources.  This work proposes several new and refined methodologies intended to assist during all stages of circuit design.  First, an algorithm has been developed to automatically determine circuit analytical solutions from a user-defined circuit configuration.  This analytical solution may then be used to rank circuits by traditional derivative-based linear circuit analysis or one of several newly proposed objective functions, including a yield indicator (the yield score) or a value-based indicator (the moment of inertia). Second, this work presents a four-reactor flotation model which considers both process kinetics and machine carrying capacity.  The simulator is suitable for scaling laboratory data to predict full-scale performance.  By first using circuit analysis to reduce the number of design alternatives, experimental and simulation efforts may be focused to those configurations which have the best likelihood of enhanced performance while meeting secondary process objectives.  Finally, this work verifies the circuit analysis methodology through a virtual experimental analysis of 17 circuit configurations.  A hypothetical electrostatic separator was implemented into a dynamic physics-based discrete element modeling environment.  The virtual experiment was used to quantify the selectivity of each circuit configuration, and the final results validate the initial circuit analysis projections. / Ph. D.