Water distribution systems throughout the United States are in various and uncertain stages of deterioration. Large capital expenditures are needed for their maintenance, modernization, and revitalization. Failures of the systems to supply adequate flow and pressure are adverse to the long-term economic growth and prosperity of the nation. Modeling the uncertain capacity of the distribution network is essential to allocating limited resources to components requiring the most rehabilitation. Network capacity and reliability are related to the uncertain conditions of pipes in the system. Some approaches to measuring a hydraulic capacity have been based on specifying flow volume alone without accounting for pressure. This paper introduces the combining of requirements for volume and pressure in a single dimension, the hydraulic power. Next, the hydraulic power capacity is defined as the probability that there exists a feasible flow of hydraulic power in the water distribution network. The probabilistic assessment of hydraulic power capacity is demonstrated in a small example under the assumptions of (1) fixed, known maximum inflows (supply) and minimum outflows (demand), (2) uncertain capacities for hydraulic power in individual pipes, reflecting uncertain conditions of pipe decay and roughness, and (3) an optional operating rule corresponding to a fixed minimum total loss of power in the network. ¿ 1998 American Geophysical Union