In this paper, we propose an epoch-making soft sheet actuator called “Wavy-sheet”. Inspired by gastropod’s locomotion, Wavy-sheet can generate continuous traveling waves on the whole soft body. It aims to be applied to a mobile soft mat capable of moving and transporting without damaging the object and the ground. The actuator, driven by pneumatics, is mainly composed of a couple of flexible rubber tubes and fabrics. The advantages are: i) many traveling waves can be generated by just three tubes, ii) the whole structure can adapt its own shape to the outer environment passively, and iii) only 10 mm in thickness can generate the waves with larger than 10mm in amplitude. In this paper, first, we describe the basic concept of the Wavy-sheet, and then show the configuration and the principle of wave propagation. Next, fabrication methods are illustrated and the design methods are addressed. By using a prototype actuator, several experiments are conducted. Finally, we verify the effectiveness of the proposed actuator and its design methods.