Underwater robots are useful for exploring valuable resources and marine life. Traditional underwater robots use screw propellers, which may be harmful to marine life. In contrast, robots that incorporate the swimming principles, morphologies, and softness of aquatic animals are expected to be more adaptable to the surrounding environment. Rajiform is one of the swimming forms observed in nature, which swims by generating the traveling waves on flat large pectoral fins. From an anatomical point of view, Rajiform fins consist of cartilage structures encapsulated in soft tissue, thereby realizing anisotropic stiffness. We hypothesized that such anisotropy is responsible for the generation of traveling waves that enable a highly efficient swimming. We validate our hypothesis through the development of a stingray robot made of silicone-based cartilages and soft tissue. For comparison, we fabricate a robot without cartilages, as well as the one combining soft tissue and cartilage materials. The fabricated robots are tested to clarify their stiffness and swimming performance. The results show that inclusion of cartilage structure in the robot fins increases the swimming efficiency. It is suggested that arrangement and distribution of soft and hard areas inside the body structure is a key factor to realize high-performance soft underwater robots.