To analyze mode fields in a seven-folded stable resonator with circular diaphragms, we introduce a new method combining the traditional self-reproducing theory with diffraction theory in the form of the ray matrix. Since the iterative method presented by Fox and Li is complex for the seven-folded resonator with diaphragms, in this paper, by means of Collins's formula in polar coordinates, diffraction integral equations expressed by ray matrices are converted to finite-sum matrix equations along diffraction interfaces. Moreover, diaphragms and reflective areas in the seven-folded resonator are simplified to apertures given by the pupil function. Finally, using the self-reproducing principle, we describe mode fields and their losses in the folded resonator as eigenvectors and eigenvalues of a transfer matrix. By calculating the eigenvectors and eigenvalues of the transfer matrix, we obtain eigenmode field distributions and their losses in the resonator. It is shown from simulation results that the seven-folded resonator with circular diaphragms can easily yield the fundamental mode, so it can output laser beams of good quality.