A strict proof of the hyperbolicity of the multi-class LWR (Lighthill-Whitham-Richards) traffic flow model, as well as the descriptions on those nonlinear waves characterized in the traffic flow problems were given. They were mainly about the monotonicity of densities across shocks and in rarefactions. As the system had no characteristic decomposition explicitly, a high resolution and higher order accuracy WENO (weighted essentially non-oscillatory) scheme was introduced to the numerical simulation, which coincides with the analytical description.
