**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 $M\to\infty$.