As the technology of robotics intelligence advances, and new application areas for mobile robots increase, the need for alternative fundamental locomotion mechanisms for robots that allow them to maneuver into complex unstructured terrain becomes critical. In this research we present a novel locomotion mechanism for mobile robots inspired by the motility mechanism of certain single celled organisms such as amoebae. Whole Skin Locomotion (WSL), as we call 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. This research presents the preliminary analytical study towards the design and development of the novel WSL mechanism. In this thesis we first investigate how amoebas move, then discuss how this motion can be replicated. By applying the biological theories of amoeboid motility mechanisms, different actuation models for WSL are developed including the Fluid Filled Toroid (FFT) and Concentric Solid Tube (CST) models. Then, a quasi-static force analysis is performed for the CST model and parametric studies for design, including power