The influence of surface roughness in crack face on the behavior of crack growth is studied. Numerical results derived from two kinds of mechanical models representing the macroscopic and microscopic asperity supposed to exist in the face of an initial crack are compared. In macro-asperity model, the influence of location and size of single-triangular asperity on the stress intensity factor is evaluated. In this model, it is found that the mode-I stress singularity appears in certain circumstances even under overall compression. In micro-asperity model, influence of friction coefficient on the trajectory of crack path is discussed. There exists a tendency that a path of wing crack growth becomes more straight and parallel to axis of compression as the friction coefficient increases.