The main goal of this work is the comparison of the size of the plastic zone at the crack tip for two analysis methods: an analytical linear method and an elastic-plastic analysis employing the Finite Element method (ANSYS software). All calculations were made for a crack loaded under pure shear modes. These types of loading are not sufficiently described in the literature. The first part of this work introduces the problem with the crack tip plastic zone using both linear and nonlinear fracture parameters. The second part is dedicated to the construction of the Finite Element model in the ANSYS software. The geometry of the samples and the loading levels were chosen to match an existing experimental test of the impact of shear modes on the crack behavior. In the third part of this thesis, the plastic zone radii for pure shear modes II and III are estimated using several methods and the results are compared. In the last part of this work, the same procedure as in the previous part is applied on a mixed-mode II+III loading. A result of this thesis is the assessment of the application limits of the linear analysis method used to estimate the size of the plastic zone at the crack tip for a specific geometry and material model.