A stress-strain state of the elastoplastic material around a circular hole under localization of shear strain on the equiangular spirals from different families is considered. The shear lines are modeled by cuts with conditions on them providing the possibility of appearing of discontinuities in shear displacements. An elastoplastic material stress-strain behavior outside the shear bands is proposed. A finite element method is used for numerical modeling this problem. The contour lines of maximum shear stresses for different location of shear lines in the domain are constructed.