The gas exchange process is essential for the breathing performance of an IC(internal combustion) engine. The numerical model is presented which calculates the behavior of unsteady gas flow and pressure wave propagation through the engine duct system for predicting the performance as well as the radiated orifice noise due to the fluctuating flows. The quasi-one-dimensional flow analysis through the duct system leads to the flow network formulation. Primary elements of the network are straight ducts, open terminations, chambers and connected junctions. The duct flow is modeled by the unsteady Euler equation and numerically treated with an ENO(Essentially-Non-Oscillatory) scheme. The connected junction with a sudden area change between two ducts and the branched junction of multiple ducts are frequently encountered in the flow network. The boundary conditions of one-dimensional unsteady compressible flow at the two types of junctions are intensively studied. The boundary conditions for the junctions are usually implemented by considering quasi-steady balances(mass, energy, etc.) through the junctions in conjunction with the transported characteristic information inside ducts. The quasi-steady balances yield the system of non-linear algebraic equations. The iterative solution procedure of the equations, however, causes the problems of the divergence and multiple solutions. In order to overcome the difficulties, new quasi-linear equations are formulated by differentiating the balance equations in time. Introducing the Thompson’s characteristic approach, higher order accuracy is archived on and near the boundaries. A typical correction procedure and high order time integration are also employed for the numerical stability. The new boundary condition, therefore, requires a non-iterative solution procedure that results in a unique solution and a smaller computational effort. The one-dimensional gas dynamics code, in which the new boundary condition is implemented, is developed for the unsteady flow in the internal combustion engines as well as a general ducting system. The computer code is applied to the shock tubes with a branched junction, expansion chamber and Helmholtz resonator. The calculation result shows a good agreement with measurement data. The numerical robustness with a large pressure amplitude range and the computing time saving are also shown. Finally, application to the IC engine is carried out. The duct pressure and radiated sound pressure are compared with measurement data and multi-dimensional calculation data. And the noise control process of multi-cylinder engine is demonstrated.