Abstract: The talk is based on a joint work with E. Stockmeyer. We consider a two- dimensional Dirac operator in a bounded domain and discuss boundary conditions, which can be imposed to define a self-adjoint operator.We give a mathematically rigorous proof of the fact, that the spectrum of the Dirac operator defined in $L_2(R^2;C^2)$ with the mass equal to zero inside a bounded region $\Omega$ and M outside converges to the spectrum of the Dirac operator with zero mass defined on $L2(\Omega ;C^2)$ with the so-called infinite mass boundary condition as $M\to\infty$.