<p>This study presents a continuum dynamic framework for modeling the rectilinear locomotion of a segmented earthworm-like robot, with the goal of bridging discrete and continuous modeling paradigms. Beginning from a discrete dynamic model that captures segment-level actuation and frictional interactions, a continuum model is derived via approximation based on a shift operator. In this continuum formulation, both discrete gait actuation and phase-coordination control—each characterized by retrograde peristaltic wave propagation—are represented as traveling strain waves along the robot body. This approach facilitates efficient analysis of the robot’s global behavior while preserving the essential mechanics of metameric actuation and anisotropic friction. The continuum model is then applied to investigate the locomotion performance under various control schemes. Comparative simulations demonstrate strong consistency between the continuum and discrete models, validating the continuum framework’s accuracy in capturing key dynamic phenomena. The model successfully predicts performance degradation due to backward slippage induced by dry friction and limitations arising from insufficient actuation force. Parameter studies further reveal that increasing the anchoring ratio and enhancing friction anisotropy effectively mitigate backward slippage, while a longer actuation wavelength can significantly improve locomotion efficiency. Overall, the proposed continuum model provides a unified and computationally tractable framework for the dynamic analysis and control of soft, worm-like robots. These insights have practical implications for the design and deployment of worm-inspired robots in confined or dynamically changing environments.</p>