AbstractAn approach to reducing the cost of drainage networks, such as plumbing networks in buildings, is described. The drain design problem is modelled as a specialized mathematical network called a drainage network; it is shown to be related to the Steiner problem in a directed graph. A procedure which yields a good approximation to the minimum cost drainage network is described. The theoretical solution is implemented in practice via an interactive computer routine which allows for the network to be fitted to the real building. Examples of the application of the approach are given.