Advanced manufacturing systems such as Flexible Manufacturing Systems (FMSs) are capital-intensive. Designing functional yet cost-effective FMSs is a challenging task because it involves the solution of a complex series of interrelated problems. In this paper, we study a design problem for FMSs that consist of multiple types of machines. Using closed queueing network models for FMSs, this problem seeks the minimum cost design subject to meeting throughput requirements. The design decisions include the number of machine groups, the number of machines for each group, the workload allocation among machine groups, the number of pallets, the number of transporters, and the batch size. Since these design decisions are highly interdependent, we present the optimum and heuristic methods that simultaneously determine them. To our knowledge, these methods are the most general analytical methods for FMS design. Development of the heuristic methods is crucial because of the time-consuming nature of the optimum method as the number of machine types increases. Computational results show that the heuristic methods are both effective and efficient.