Recently, some statistical studies have been done using the shape data. One of these studies is clustering shape data, which is the main topic of this paper. We are going to study some clustering algorithms on shape data and then introduce the best algorithm based on accuracy, speed, and scalability criteria. In addition, we propose a method for representing the shape data that facilitates and speeds up the shape clustering algorithms. Although the mentioned method is not very accurate, it is fast; therefore, it is useful for datasets with a high number of landmarks or observations, which take a long time to be clustered by means of other algorithms. It should be noted that this method is not new, but in this article we apply it in shape data analysis.