Abstract: We look at a class of Dirac operators with a potential that can be interpreted as masses in separated regions of the space. These operators arise naturally in the study of the MIT bag model in three dimensions, and one can generalize their construction to higher dimension. We are interested in the behavior of the operator's eigenvalues in several asymptotic regims when the masses go to infinity. It can be shown that there is an effective operator on the boundaries of the regions previously considered which governs the convergence of the spectrum.