The Ritz method is used to calculate eigenmodes and eigenfrequencies in a continuum model of the vocal folds. The investigation represents a rectification and extension of previous studies, emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system. Concurring with previous assertions, two of the lower-order eigenmodes are theorized to play a major role in facilitating self-oscillation of the folds during phonation. One mode, related to vertical phasing, is shown to have a more direct control over glottal convergence/divergence than indicated in previous calculations. Unlike lumped element models, the continuum model predicts that the eigenfrequencies of the two modes are closely spaced over an extensive range of tissue sizes and stiffnesses. This finding may help explain why the two modes entrain so naturally over a wide range of phonatory adjustments in human phonation.