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The nematode Caenorhabditis Elegans has become an important model organism for many areas of biological research including genetics, development, and neurobiology. It is the first organism to have its genome sequenced, complete cell ontogeny determined, and nervous system mapped. With all of the information that is available on this simple organism, \emph{C. elegans} may also become the first organism to be accurately and completely modeled in silico. In this work we take a step toward this goal by presenting a biologically accurate, 3-dimensional model of C. elegans. This model takes into account many facets of the organism including size, shape, weight distribution, muscle placement, and muscle force. We also explicitly model the environment of the worm to include factors such as contact, friction, inertia, and gravity. We tuned and validated our model using video recordings taken of the worm and show that our model accurately depicts the physics of undulatory locomotion used to forward crawl on an agarose surface. We also present evidence that suggests that the forces applied by the nematode during locomotion are not uniform, but decrease as the wave is propagated from its head to its tail.