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This study investigates the numerical simulation and theoretical modeling of longitudinal and transverse compressive failure in fiber reinforced composite materials.Firstly the numerical simulation of longitudinal compressive failure is conducted.The simulated results show that at one moment of the loading, the localized deformation catastrophically appears in the material, and in this initiation of the localized deformation, the reduction of tangent shear stiffness plays an important role.Based on the simulated results, the theoretical modeling of longitudinal compressive failure is implemented.A set of mathematical equations is obtained for the deformation of composite materials, and the mathematical solution of the equations is considered.There exists a state where arbitrariness appears in the solution of equations expressing deformation of composite materials, and it is indicated that the onset of arbitrariness in solution of equations expressing deformation of composite materials is closely related with the initiation of longitudinal compressive failure, and also related with the initiation of narrow localized band in the materials.Secondly the transverse compressive failure is investigated.In the numerical simulation, multiple shear bands appear in the material, and one of the shear bands develops to the entire material, and the transverse compressive failure is formed in the material.The theoretical model of transverse compressive failure shows that the critical stress value is represented by fiber volume fraction, matrix Poissons ratio, matrix yield stress and angle of shear band.Finally the numerical simulation is conducted for compressive failure in composite laminate including quasi-isotropic laminate and cross-ply laminate.The localized deformation also appears in the laminate, and the simulated deformation of the material agrees with the microscope picture of the experimental result.