We research the defects of geometric modeling in representing object attachments. It is difficult to represent different types of object attachments such as glueing or fusing in current computer graphics. We consider two types of different attachments such that an object is "put" on the top of another object, and an object is "fused" to the top of another object. To represent the relationships of object attachments, we assume a hypothesis such that we can represent the information of object attachments in computer graphics based on the cellular models, and consider the real implementation in computer graphics for proving that the cellular model of object attachments meet the hypothesis. The results of our research are expected to influence major applications including computer integrated manufacturing (CIM).