The high densities of network nodes has made spatial reuse an essential characteristic of modern wireless networks. In this paper, we evaluate the maximum throughput of Carrier Sense Multiple Access (CSMA) for Vehicular Ad-hoc Networks (VANETs) when spatial reuse is taken into account. We begin our study by extending a simple stochastic model in order to fit a VANET pattern and to obtain the spatial density of throughput in terms of the main network parameters. This model uses a Matern selection process with a random pattern of nodes distributed as a Poisson Point Process (PPP). Each node of the process receives a random mark and the nodes that have the smallest mark in their neighborhood are elected for transmission. We study both 1D and 2D network cases with an SIR (Signal over Interference Ratio) model. In order to verify the correctness of the model, extensive simulations are carried out using two simulation platforms: the network simulator, ns-3, and a simulator which is dedicated to CSMA systems. Fairly good matching between the results of the model and those obtained from simulators are observed, confirming the reliability of the theoretical model. Although the results did not perfectly match due to the number of assumptions made for the model, the results obtained nonetheless show the potential for a significant improvement in the overall throughput for VANETs and similar distributed networks.