A set of linear/nonlinear elasticity theory is examined on material modeling. In particular, crack problems are solved under each different elasticity theories. The governing partial differential equations are derived, and its hierarchy structure is discovered. A focus is on the strain energy function in which both macro and micro structure of the material can be considered. The material modeling also includes “homogeneous / nonhomogeneous” materials (e.g. functionally graded materials). Crack problems are posed and solved, and numerical results including crack displacement profiles and stress singularities in front of the crack-tip will be presented.