In this paper, we describe the design of a deformable robot with a tensegrity structure that can crawl and we show the results of experiments showing the ability of these robots to crawl. We first describe a tensegrity structure, composed of struts and cables, and its characteristics. We next explain the principle of crawling by robot body deformation, followed by a classification of the methods by which a body can be deformed and the contact conditions of the robot through the cable-graph of the tensegrity structure. We also describe topological transition graphs that can visualize crawling from each initial contact condition. We then discuss the characteristics of the proposed robot in terms of design freedom. Finally, we show experimentally that the prototype of a tensegrity robot can crawl.