The propagation of pressure waves through junctions in engine manifolds is an intrinsically multi-dimensional phenomenon. In the present work an inviscid two-dimensional model has been applied to the simulation of shock-wave propagation through 45° and 90° junctions: the results are compared with schlieren images and measured pressure-time histories. The HLLC integral state Riemann solver is used in a shock-capturing finite volume scheme, with second-order accuracy achieved via slope limiters. The model can successfully predict the evolution of the wave fronts through the junctions and the high frequency pressure oscillations induced by the transverse reflections. The calculation time is such as to make it feasible for inclusion, as a local multi-dimensional region, within a one-dimensional wave-action engine simulation.