The detrimental effects of drilling electrical steel sheets on the flux propagation and domain structure in the vicinity of a hole were experimentally studied by using Kerr microscopy. As a model system, a (110)-textured Fe-3% Si sheet sample in Epstein geometry with the preferred transverse and longitudinal axis to the working direction and a 10 mm hole in the middle of the sheet sample were chosen. Under such conditions, branched surface domains are formed in moderate magnetic fields, the orientation of which turned out to be a sensitive indicator for the local effective field, thus allowing to visualize the flux propagation and degradation around the hole. It was also found an interesting way to use the orientation of the surface domains at the presence of an applied magnetic field as an indicator for the local effective field direction. Since the reluctance was growth depending upon decreasing cross-sectional area in the sides of the non-magnetic region, rapid saturation was able to observe by the evaluation of magnetic domains.