The plasticity theory is used in order to dimension the structures more rationally and to reduce the self-weight of the structures. On the other hand, the calculation according to elasticity theory is based on results obtained in a critical cross section of the structure. However, it has been proven by practice that a structure can withstand local overloads if it is statically indeterminate, which in reality is valid for most structures. Local load bearing failures in critical cross sections of the structure can be described as formation of plastic hinges. Different types of structural actions can cause plastic hinges. For this reason, this thesis elaborates several ways of cross section plasticization: torsion, pure bending, bending with forces and bending combined with axial load. The application of plasticity theory is carried out on the basis of static and kinematic theorems. This thesis presents the solution of a statically indeterminate structure by means of a kinematic theorem, i.e. by using virtual displacements principle. Possible cases of the kinematic mechanism formation are shown. The end result is presented in the form of the value of the relevant allowable load at which the most probable kinematic mechanism will form.