The three-dimensional effects near crack-tips and crack-tip fields of brittle damaged materials are investigated in this paper. The main results are as follows:1. An infinite plate containing a finite through crack under tensile loading is analyzed by using Fourier transform based on the Kane-Mindlin kinematic assumptions. The variation of SIF with plate thickness is obtained and the size of 3D deformation zone near the crack tip is evaluated as three-fourths of plate thickness.2. A new FEM formulation based on the K-M assumptions including transverse shear effects is first presented. The K-M assumptions are extended to elastic-plastic problems and the corresponding FEM formulation is established. The computational results show that the 3D deformation zone is confined within the extent of two of plate thickness near the crack tip when the ratio of plastic tangential modulus E_t to Young’s modulus E is greater than O.2.3. The asymptotic near-tip stress, strain and damage fields for a modeⅢcrack and a mode I crack in an incompressible medium are obtained according to the Mazars’s damage model for concrete. A simplified damage model for concrete is proposed and an exact solution for a modeⅢcrack is obtained based on the simplified model under the small scale damage conditions. Finally, the near-tip fields for a modeⅢcrack in a creeping damaging material is tentatively analyzed.