Numerous soft robots that mimic living organisms have been proposed. Earthworm robots are a type of robots that imitate the peristaltic locomotion of earthworms. Engineering reproduction of the burrowing motion of earthworms is useful for soil investigation and stirring of the particles in the soil. In this study, a novel compact actuation system that can be mounted on small earthworm-like robots was developed. The system can output axial extension force and is suitable for enabling earthworm-like robots to drive peristaltic locomotion in soil. The actuation system for an earthworm robot was fabricated by reproducing the hydrostatic skeleton and circumferential muscle arrangement of the earthworm using a water-filled rubber-like resin and shape memory alloy (SMA). We confirmed that the proposed system can output the axial extension force by applying an electric current to the SMA of the actuation system. Thus, the fabricated actuation system is useful for earthworm-like robots that dig holes. This system can be extensively used in earthworm-like as well as small soft robots to easily obtain the extension force.