The formulation of a mathematical model to predict transient flows in hydraulic networks is presented. The network formulation consists of breaking the network into a series of connected reaches; reducing the finite difference equations for each reach into two "reach" equations; forming an exterior matrix consisting of the reach equations, external boundary conditions, and interior compatibility conditions; solving the external matrix for the end values of discharge and water surface elevation for all reaches and back-substituting for all interior values. Examples presented include the James River, USA, estuary model (twenty-four nodes and twenty-six reaches), the Cork Harbour, Ireland, estuary (thirteen-reach, double-looped network), and the Rio Bayamon basin, Puerto Rico. Results are very satisfactory when compared to known data.