The Ritz method is used to calculate the eigenmodes and eigenfrequencies of a 3-D vocal foldlike continuum. The investigation represents a rectification and extension of previous studies [I. R. Titze and W. J. Strong, J. Acoust. Soc. Am. 57, 736--744 (1975); I. R. Titze, J. Acoust. Soc. Am. 60, 1366--1380 (1976)], emphasizing the indispensability of utilizing natural boundary conditions when computing the characteristic modes of a system. Concurring with previous assertions, two of the eigenmodes are theorized to play a major role in facilitating self-oscillation of the vocal folds. For the case of incompressible tissues, the eigenfrequencies of the two eigenmodes are nearly identical throughout a large parameter space spanned by the mechanical constants. If truly indicative of mechanisms governing vocal fold dynamics, it may help explain why the two eigenmodes entrain so naturally across a wide range of phonatory adjustments.