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This thesis presents a unified modeling and simulation framework for analyzing sidewinding and tumbling locomotion of the COBRA snake robot across rigid, compliant, and granular terrains. A contact-implicit formulation is used to model distributed frictional interactions during sidewinding, and validated through MATLAB Simscape simulations and physical experiments on rigid ground and loose sand. To capture terrain deformation effects, Project Chrono’s Soil Contact Model (SCM) is integrated with the articulated multibody dynamics, enabling prediction of slip, sinkage, and load redistribution that reduce stride efficiency on deformable substrates. For high-energy rolling locomotion on steep slopes, the Chrono DEM Engine is used to simulate particle-resolved granular interactions, revealing soil failure, intermittent lift-off, and energy dissipation mechanisms not captured by rigid models. Together, these methods span real-time control-oriented simulation and high-fidelity granular physics. Results demonstrate that rigid-ground models provide accurate short-horizon motion prediction, while continuum and particle-based terrain modeling becomes necessary for reliable mobility analysis in soft and highly dynamic environments. This work establishes a hierarchical simulation pipeline that advances robust, terrain-aware locomotion for robots operating in challenging unstructured settings.