A method is proposed for modeling the interaction of fields of quantum electrodynamics (QED) with two-dimensional materials in the framework of the Symanzik approach. It is based on the modification of the QED Lagrangian with additional contribution concentrated in a two-dimensional
region of space. The requirement do not violate in this way the basic principles of QED imposes significant restrictions on the possible form of the modified Lagrangian and as a result it appears in the model a small number of new dimensionless parameters describing the material properties
of a two-dimensional object. The Dirac spinor fields in this approach can be used to describe the processes of interaction of 1/2-spin particles (electrons, protons, neutrons) with two-dimensional materials. Results obtained in the model of interaction of spinor fields with a homogeneous isotropic material plane are presented.