Transmission losses of various reactive silencers are predicted, using a time accurate finite difference method. The numerical scheme is the 3rd order upwind scheme for axisymmetric Euler equations. Main advantage of the present method is that it can simulate linear and non-linear wave propagation phenomena in a flow field directly with minimum numerical oscillation errors. The special treatments of incident wave condition, i.e. multiple harmonics of the transparent acoustic condition are applied to the transmission loss prediction for calculation efficiency. For the validation of the present approach, circular expansion chamber silencers without mean flow and an exponential pipe with mean flow are simulated in case of linear incident wave. The computed transmission losses have quite good agreements with those of the others. The nonlinear incident wave case is also investigated to check the usefulness of this method. The periodic N wave is clearly captured without numerical oscillation errors, and the insertion losses of two different incident frequencies are compared.