This book presents original mathematical models of phase-transformation stresses in composite materials, along with mathematical models of phase-transformation induced micro-/macro-strengthening and intercrystalline or transcrystalline crack formation. The mathematical determination results from mechanics of an isotropic elastic continuum. The materials consist of an isotropic matrix with isotropic ellipsoidal inclusions. These stresses are a consequence of the difference between dimensions of crystalline lattices, which are mutually transformed during the phase-transformation process in the inclusions or the matrix. The mathematical models include microstructural parameters of a real matrix-inclusion composite, and are applicable to composites with ellipsoidal inclusions of different morphology (e.g., dual-phase steel, martensitic steel). In case of a real matrix-inclusion composite, such numerical values of the microstructural parameters can be determined, which result in maximum values of the micro- and macro-strengthening, and which define limit states with respect to the intercrystalline or transcrystalline crack formation in the matrix and the ellipsoidal inclusion.