A new technique for the calculation of the transient or the steady-state mass flow rate and pressure distribution in incompressible flow networks is presented. Employing the matrix method of network analysis, the nodal continuity and branch momentum equations are solved simultaneously to obtain explicit relations giving the unknown nodal pressures and branch mass flow rates. In this manner, the transient or the steady-state behavior of incompressible flow networks with arbitrary configuration having nodal sources and sinks as well as branch transducers can be determined. In contrast with the conventional steady-state network analysis methods, the new technique can be extended to the unsteady analysis of compressible flow in networks having an arbitrary configuration with heat transfer and phase change. To ascertain the accuracy of the solution, a numerical stability and convergence analysis is performed which provides an estimate for the upper bound of the time for the increment needed for a stable and convergent solution. The new technique can be applied to the treatment of transient problems such as flow coastdown studies resulting from loss of pumping power in nuclear water reactors, hydraulic transients of the cooling system, for large steam power plants as well as the steady-state analysis of water distribution networks. The latter application is demonstrated in this study.