||We present a procedure for generating a coarse, high-quality, tetrahedral mesh whose exterior surface encloses and approximates a given triangle mesh. A tetrahedral mesh is useful for computing perturbation of the triangle mesh based on continuum mechanics: perturbation such as plastic flow, fracture, and elastic deformation. The computer graphics community has long used this physics-based simulation to produce animations of objects exhibiting such physical phenomena. Interactive animation applications such as industrial design, medical training, and computer entertainment require meshes that are particularly efficient and robust, and our meshing procedure targets these properties. We begin with a BCC background lattice and sculpt an initial mesh from it whose tetrahedra occupy some of the volume bounded by the triangle mesh. We then refine this initial mesh with an iterative optimization procedure that simultaneously minimizes the distance from the triangle mesh to the surface of the tetrahedral mesh and maximizes the numerical quality of the tetrahedra. Our procedure provides a trade-off among the mesh's quality, resolution, and degree of approximation of the triangle mesh.