AbstractThis study presents some features in the numerical modelling of multi‐class mixed freeway traffic described by extended LWR model. The evaluation of the eigenvalues and the right characteristic matrix of the mixed traffic system was reported in detail. To some extent, this is the key step in the application of the second‐order symmetrical total variation diminishing (TVD) numerical method to traffic modelling. Examples for four‐class mixed traffic flows were given to illustrate the solution feasibility. It was found that, when the global density wave keeps the same form, the variation of vehicular composition in the initial density wave has no effect on the mean speed of propagation of traffic wave on freeways, but can affect the decay rate of the density wave in different way. Traffic mixing and the impedance of the slow moving vehicles are reasons of the small amplitude density oscillations downstream the main global density wave. Copyright © 2005 John Wiley & Sons, Ltd.