This paper develops a general model and advances a solution methodology for the optimum design of natural gas transmission networks. The complete static design problem addressed is that of determining the optimum number, locations, sizes, and operating characteristics of the components of the system by minimizing, over a finite time horizon, T, the present worth of costs such that no pressure or technological specifications are violated. Most published investigations of this problem have resulted in suboptimal solutions because they fixed a subset of the decision variables while optimizing the others. This work differs from that of previous attempts at the complete problem in that it includes the option of expanding an existing network; it considers more general cost functions and the solution times have been so reduced that larger problems and extensive sensitivity analyses can be investigated.