Local approach of fracture in damage mechanics based on an anisotropic damage tensor in applied to analyse the anisotropic aspect of crack problems. The stress analyses of a plane stress model with a crack inclinated toward the load direction were conducted to evaluate the validity of the damage tensor. The results of the FE analysis using the present model were compared with those by the standard code. Although some differences were found between the present and the conventional analyses at the crack tip probably owe to the F. E. approximation, good agreements were obtained between them in general.