This paper presents an algorithm to generate quality tetrahedral meshes for the volumes bounded by the molecular skin model defined by Edelsbrunner. The algorithm applies the Delaunay refinement to the tetrahedral meshes bounded by quality surface meshes. In particular, we iteratively insert the circumcenters of bad shape tetrahedra with a priority parameterized by its distance from the surface. We achieve a bounded radius-edge ratio for the tetrahedral mesh after the refinement. Finally, we apply the sliver exudation algorithm to remove ‘slivers'. The algorithm terminates with guarantees on the tetrahedral quality and an accurate approximation of the original surface boundary.