A method for understanding convex objects is presented. Convex objects frequently appear in many fields of research and engineering. Research into the problem of understanding convex objects has been carried out as part of wider investigations related to the method of shape understanding, implemented as a shape understanding system (SUS). The main novelty of the presented method is that the process of understanding a convex object is related to the visual concept represented as a symbolic name of the possible classes of shapes. The possible classes of shapes are viewed as a hierarchical structure, where at each level of description the different aspects of shape are incorporated into the shape model. The new "intelligent" way of processing is proposed, in which at each stage of the reasoning process that leads to assigning an examined object to one of the possible classes, the specialized processing methods are used. These methods are very efficient because they deal with a specific class of objects. The proposed shape understanding system is designed to interpret visual data in terms of shape properties to perform tasks that require higher levels of understanding capabilities.