A stress-strain state of the material around a circular working 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 elastic material stress-strain behavior outside the shear bands is proposed. A finite element method is used for numerical modeling this problem. The fields of displacements and stresses for domains with different numbers of shear lines are constructed.