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Vehicular Ad Hoc Networks (VANETs) with base stations are called hybrid VANET, where base stations are deployed to improve the throughput capacity. In this paper, we study the multicast throughput capacity for hybrid wireless VANET with a directional antenna on each vehicle and the end-to-end delay is constrained. In the hybrid VANET, there are n mobile vehicles (or nodes) distributed in a unit area with m strategically deployed base stations connected using high-bandwidth wire links. There are n_s multicast sessions and each multicast session has one source which transmits identical data to its associated p destinations. We investigate the multicast throughput capacity for two mobility models with two mobility scales, respectively, while each vehicular node is equipped with a directional antenna and with a tolerant delay D. That is, a source node transmits to its p destinations only with the help of normal nodes within D consecutive time slots. Otherwise, the transmission will be performed with in the infrastructure mode, i.e., with the help of base stations. We demonstrate that the one dimensional i.i.d. slow mobility pattern catch the main feature of VANETs. And we find that the multicast throughput capacity of the hybrid wireless VANET greatly depends on the delay constraint D, the number of base stations m, and the beamwidth of directional antenna θ. In the order of magnitude, we obtain the closed form of the multicast throughput capacity of the hybrid directional VANET, where the impact of D, m and θ on the multicast throughput capacity is analyzed. Moreover, we derive the lower bound of the muticast throughput using a similar raptor coding approach.