The development of the technology and connected devices such as internet of things (IoT), internet of vehicles (IoV), and 5G motivate the researchers to give more attention in the field. Clustering is a key factor in vehicular ad-hoc network (VANET) where a number of vehicles join to form a group based on common characteristics. Vehicles are distinguished by their high mobility in ad hoc vehicle networks. Changes frequently occur in the topology of VANET, causing continuous failures in network communication. In such a dynamic environment, the creation and maintenance of a stable cluster are significant challenges. The evaluation of stability in VANET clustering is an important part to evaluate the clustering approaches. In this paper, a mathematical technique (based on the birth-death process) is created to evaluate the clusters stability based on the number of leaving and joining vehicles to each cluster after its creation. The stability of the created clusters is tested by checking the number of vehicles in each cluster at different successive times. These tests indicate the joining and leaving vehicles to each cluster and their effects on the cluster stability. When the results of the technique show that the standard deviation is small for each cluster, it can be concluded that the proposed clustering algorithm is able to achieve stability in cluster maintaining phase.