Soft robotics offers the unique promise of creating inherently safe and adaptive systems. These systems bring man-made machines closer to the natural capabilities of biological systems. An important requirement to enable self-contained soft mobile robots is an on-board power source. In this paper, we present an approach to create a bio-inspired soft robotic snake that can undulate in a similar way to its biological counterpart using pressure for actuation power, without human intervention. With this approach, we develop an autonomous soft snake robot with on-board actuation, power, computation and control capabilities. The robot consists of four bidirectional fluidic elastomer actuators in series to create a traveling curvature wave from head to tail along its body. Passive wheels between segments generate the necessary frictional anisotropy for forward locomotion. It takes 14 h to build the soft robotic snake, which can attain an average locomotion speed of 19 mm s(-1).