The failure behavior of brittle solids under compressive stresses is discussed. It is known that the failure mode of brittle solids under compressive stresses depends strongly upon specimen geometry and loading conditions. A plate specimen often exhibits a split-type fracture characterized by mode I cracks that propagate almost parallel to the direction of compression. On the other hand, a pseudo-mode II fracture in which the failure plane is inclined from the axis of compression can be observed in a compression test of a cylindrical specimen. In the uniaxial compression test of plate-type mortar and PMMA specimens, the macroscopic fracture was dominated by the appearance of mode-I wing cracks and their propagation. However, in a neighborhood of an artificial crack tip, a considerable damage zone was also observed. In order to investigate the mechanism for a formation of damage zone, numerical analyses base on the linear elastic fracture mechanics were carried out. It was found that the damage zone is composed of an echelon of mode I micro-surface cracks and the inclination of the damage zone is about 30degrees from the axis of compression.