Manufacturing system design decisions are costly and involve significant investment in terms of allocation of resources. These decisions are complex, due to uncertainties related to uncontrollable factors such as processing times and part demands. Designers often need to find a robust manufacturing system design that meets certain objectives under these uncertainties. Failure to find a robust design can lead to expensive consequences in terms of lost sales and high production costs. In order to find a robust design configuration, designers need accurate methods to model various uncertainties and efficient ways to search for feasible configurations. The dissertation work uses a multi-objective Genetic Algorithm (GA) and Petri net based modeling framework for a robust manufacturing system design. The Petri nets are coupled with Bayesian Model Averaging (BMA) to capture uncertainties associated with uncontrollable factors. BMA provides a unified framework to capture model, parameter and stochastic uncertainties associated with representation of various manufacturing activities. The BMA based approach overcomes limitations associated with uncertainty representation using classical methods presented in literature. Petri net based modeling is used to capture interactions among various subsystems, operation precedence and to identify bottleneck or conflicting situations. When coupled with Bayesian methods, Petri nets provide accurate assessment of manufacturing system dynamics and performance in presence of uncertainties. A multi-objective Genetic Algorithm (GA) is used to search manufacturing system designs, allowing designers to consider multiple objectives. The dissertation work provides algorithms for integrating Bayesian methods with Petri nets. Two manufacturing system design examples are presented to demonstrate the proposed approach. The results obtained using Bayesian methods are compared with classical methods and the effect of choosing different types of priors is evaluated. In summary, the dissertation provides a new, integrated Petri net based modeling framework coupled with BMA based approach for modeling and performance analysis of manufacturing system designs. The dissertation work allows designers to obtain accurate performance estimates of design configurations by considering model, parameter and stochastic uncertainties associated with representation of uncontrollable factors. Multi-objective GA coupled with Petri nets provide a flexible and time saving approach for searching and evaluating alternative manufacturing system designs.