In this paper, a locomotion mechanism for mobile robots inspired by how single celled organisms use cytoplasmic streaming to generate pseudopods for locomotion is presented. Called the whole skin locomotion, it works by way of an elongated toroid, which turns itself inside out in a single continuous motion, effectively generating the overall motion of the cytoplasmic streaming ectoplasmic tube in amoebae. With an elastic membrane or a mesh of links acting as its outer skin, the robot can easily squeeze between obstacles or under a collapsed ceiling and move forward using all of its contact surfaces for traction, even squeezing itself through holes of a diameter smaller than its nominal width. Therefore this motion is well suited for search and rescue robots that need to traverse over or under rubble, or for applications where a robot needs to enter into and maneuver around tight spaces such as for robotic endoscopes. This paper summarizes the many existing theories of amoeboid motility mechanisms and examines how these can be applied on a macroscale as a mobile robot locomotion concept, illustrating how biological principles can be used for developing novel robotic mechanisms. Five specific mechanisms are introduced, which could be implemented to such a robotic system. Descriptions of an early prototype and the preliminary experimental and finite element analysis results demonstrating the feasibility of the whole skin locomotion strategy are also presented, followed by a discussion of future work.