In this thesis cracked anisotropic elastic bi-material plates under bending are considered. Correspondence relationships between plate stretching and bending problems are utilized to investigate the stress singularities at the tip of an interface crack. The relationships are also used to compute the stress intensity factors for multiple internal cracks under remote uniform bending. In computing the stress intensity factors cracks are regard as continuous distributions of dislocations to establish integral equations relating dislocation densities with the applied moment. Gauss-Chebyshev quadrature is used to convert integral equations to algebraic equations. The numerical examples include infinite plates containing one and two cracks under uniform bending; isotropic as well as orthotropic materials are considered.