Vehicular ad hoc networks (VANETs) are emerging to serve various types of applications for serving smart cities and intelligent transportation systems. There are several challenging factors for ensuring reliable and stable VANETs communications. VANETs clustering is essential functionality to serve routing protocols and enable reliable VANETs. Clustering algorithms for VANETs operate in a decentralized mode, which requires incorporating additional stages before deciding the clustering decisions and might create sub-optimality due to the local nature of the decentralized approach. In addition, the challenging architecture of the road environment can cause confusing clustering decisions. This problem becomes more challenging due to the evolving nature of clusters in VANETs in general and in 3D VANETs in particular. This paper attempts to solve the problem of VANETs in 3D road environments using a centralized clustering technique to develop a Cauchy density model. The model has been simulated by considering several simulation parameters including traffic, mobility, driving behavior, and road curvature. The simulator also includes an adjacency list that defines the road's points and straight-line segments. The clustering technique of the Cauchy density model determines the mobility vector to enable adding vehicles to their respective clusters. The simulator has been implemented in MATLAB to perform complex scenarios in three locations of 3D road environments. A comparison with selected benchmarks shows the superiority of our model over the benchmarks models in which our model achieves an improvement percentage of 1, 10, and 3 for average cluster head duration, average cluster member duration, and clustering efficiency, respectively. © 2013 IEEE.