Flow in branching pipes is a well-known hydraulics problem that is traditionally assigned to mechanical, civil and chemical engineering students in their fluid mechanics introductory course. The conventional solution procedure advocated by fluid mechanics and hydraulics textbooks is based on a tedious trial-and-error approach. Although manageable for a simple system of three pipes, the procedure becomes impractical for larger number of pipes. A recent numerical algorithm attempted to eliminate the trial-and-error approach; however, the procedure still requires an explicit step for identifying the discharging tanks from the filling ones. In the present study, an efficient numerical algorithm based on a Newton linearization procedure is developed which would eliminate the above mentioned drawbacks. The efficiency of the new procedure is demonstrated by solving a simple three-pipe problem and a more complicated nine-pipe problem. The results of the present algorithm are validated against available results in the literature and against the piping software package, EPANET. The proposed procedure could be implemented in a straightforward manner through the MATLAB environment. ß 2015 Wiley Periodicals, Inc. Comput Appl Eng Educ 23:537-541, 2015; View this article online at wileyonlinelibrary.com/journal/ cae;