Metal matrix composites (MMCs) are going to be used for structural components or functional parts which require high specific stiffness and strength at elevated temperature. In particular, MMCs reinforced with particulates, whiskers and short fibers have the merit that they are manufactured by similar processes for common metals. This kind of MMCs are, of course, more expensive than common metals. Therefore, MMC parts should be designed so as to make full use of its anisotropic stiffness and strength. Thus, the stresses in the parts should be analyzed by FEM or BEM. Even to analyze those elastic behavior, we must know all components of the anisotropic elastic constants of MMC.