An accurate three-dimensional (3D) mesh of biological models is fundamental for analysis and treatment simulations. Generally noninvasive magnetic resonance image (MRI) data are taken as the input for the simulation. The topologic relationship of anatomy is extracted from MR images through segmentation processes. To accelerate the biological modeling phase, template surface and volume meshes are generated based on MR images and∕or anatomical atlases (e.g., brain atlas, etc.). The boundary surfaces are extracted from segmented regions on the image slices, which are used as the input for 3D volume mesh generation. An intuitive graphic user interface was developed for biomedical applications. It integrated MRI data manipulation with surface mesh and volume mesh generators. Image volume and mesh geometries are registered in the MRI working space. As the core component of the system, a robust 3D mesh generation approach is presented. It is capable of describing irregular geometries exhibiting concave and convex surfaces. It uses deltahedral building blocks for volume mesh generation and creates high-quality, regular-shaped tetrahedral mesh elements. The approach supports multiple levels of localized refinement without reducing the overall mesh quality. The validity of this new mesh generation strategy and implementation is demonstrated via the medical applications in brain vasculature modeling, multimodality imaging for breast cancer detection, and numerous anatomically accurate models presented. Multiple material boundaries are preserved in each mesh with fidelity.