A numerical model is presented for the calculation of nonlinear waves through the branched junctions in a gas transmission pipe system. In the one-dimensional time domain analysis of the wave dynamics. the behaviour of the nonlinear waves is determined by quasi-steady boundary conditions at junctions in a pipe system. The quasi-steady treatment through the junction yields a system of nonlinear balance equations. The iterative solution procedure of the system of nonlinear equations causes the problems of divergence and multiple solutions. In order to overcome the difficulties, a new set of quasi-linear balance equations is formulated without a sacrifice of accuracy. The present model, therefore, requires a non-iterative solution procedure that results in a unique solution and a smaller computational effort. Thompson's boundary condition is used at each pipe. A new time-derivative form of balance equations, based Thompson' boundary condition, gives a set of linear algebraic equations for the balance equations. When implementing the new time-derivative form of the balance equations, corrected terms are added numerically. The present numerical model is implemented and tested for the calculation of behaviour of nonlinear waves in a branched pipe and the calculation of sound attenuation of a Helmholtz resonator and the prediction of radiated orifice noise of an internal combustion engine. Calculation results show good agreements with previous iterative calculations and measurement data. (c) 2006 Published by Elsevier Ltd.