Materials scientists and engineers use computers to investigate and solve problems in materials. If experimental investigation and theoretical analysis are called the first and the secondary method, the emerging of numerical simulations can be viewed as the third method, which is causing a structural change in scientific research and development. It promotes the cross-penetration of multiple disciplines and accelerates the transition from fundamental research to technological applications. Computational materials mechanics is a discipline that solves material-dependent mechanics problems based on the theories of materials science and mechanics, by employing modern electronic computers and numerical methods. It intersects each branch in materials science and mechanics, expands the research and applications of each branch in materials science and mechanics, and simultaneously develops its own theories and approaches.