Abstract: We generalize the phase transition model studied in [13], that describes the evolution of vehicular traffic along a one-lane road. Two different phases are taken into account, according to whether the traffic is low or heavy. The model is given by a scalar conservation law in the free-flow phase and by a system of two conservation laws in the congested phase. In particular, we study the resulting Riemann problems in the case a local point constraint on the flux of the solutions is enforced.