Since discovered in 1897, the nematode Caenorhabditis elegans has surfaced as an excellent model organism for medical and genetic research. The worm propels itself through viscous-dominated creeping flows via undulatory motion. Moreover, experiments have revealed that the netamode’s swimming gait alters as a function of fluid viscosity. In the current research, we proposed a new solid-mechanics-based auto-propulsion model featuring a closed-form displacement field that better captures the nematode’s swimming gait in water. A series of decoupled/coupled (Fluid-Structure Interaction) finite-element simulations exploiting the Arbitrary Lagrangian-Eulerian (moving mesh) technique were then conducted to investigate how different gaits affect the free-swimming speed, and how the interaction with fluids of various viscosities and the presence of wall boundaries deviate the swimming gait from the solid-mechanics-based closed-form solution.