Worm-like robots for applications including maintenance of small pipes and medical procedures in biological vessels such as the intestines, urethra, and blood vessels, have been the focus of many studies in the last few decades. The robots must be small, reliable, energy efficient, and capable of carrying cargos such as cameras, biosensors, and drugs. In this study, worm locomotion along rigid and compliant terrain is analyzed, and a novel design of worm-like multicell robots actuated by a single motor is presented. The robots employ a screw-like axis for sequencing and coordination of the cells and clamps. This design allows for significant miniaturization and reduces complexity and cost. The design of the robots and analysis of their dynamics and power efficiency are described. Two earthworm and two inchworm prototypes were built to demonstrate their performance. The robots are capable of moving forward, backward, and vertically and consume low power, which allow them to climb for hundreds of meters using onboard batteries.