Cross-media operating robots are versatile machines that can move and perform tasks in various environments such as air, water, and land. These robots are highly adaptable and flexible, making them useful in a wide range of applications, including exploration, marine research, environmental monitoring, military reconnaissance, industrial and infrastructure maintenance, and emergency response. Cross-media operating robots need to switch corresponding movement modes in different environments, such as using buoys or propellers in water and wheels or legs on land. However, existing amphibious robots often have complex structures and high maintenance costs because they rely on multiple sets of actuated systems, which leads to increased difficulty in control and longer operating times. To address these challenges, this study presents a novel wave-inspired actuated ray-inspired amphibious robot (WARAR). The WARAR design includes a wave-inspired actuated mechanism that transforms motor rotation into sinusoidal waves by passing a spiral rod through movable hinges arranged side by side, resulting in better mobility and obstacle-crossing capability. Two of these mechanisms are arranged side by side, enabling WARARs to adopt the differential principle for steering control. Based on this principle, a flexible ray-inspired fin is designed to transform the actuated force of the wave-inspired mechanisms into a propulsion force for swimming in the water by connecting the supporting bone to one end of the movable hinge and covering it with flexible silicone rubber. Moreover, by utilizing the two structures, a new type of WARAR that only requires control of the wave-inspired mechanism for operation on land, in water, and during transitions between the two is designed. Furthermore, a suitable electronic control room is designed to make the electronic control system of WARAR waterproof that can also be sealed to provide buoyancy. Specifically, WARARs are mainly fabricated through three-dimensional printing, which effectively reduces weight. The simple actuated system structure and lightweight overall machine are the keys to the high flexibility of WARARs. Moreover, the kinematic models of WARARs are established, and the swimming mode hydrodynamic characteristics of WARARs are analyzed using simulation methods. Given the complex operating environments of water and land media, a trajectory planning method is proposed using the A* planning method that considers safe areas. Finally, an experimental platform is constructed with land and water environments to test the performance of WARARs during moving, climbing, turning, and swimming. The effectiveness of the proposed trajectory planning methods for crossing water and land media is verified. Overall, the development of WARARs provides a more efficient and cost-effective solution for cross-media operating robots with applications in various fields.