The human vocal fold is treated as a continuous, transversally isotropic, bounded medium. The theory of viscoelasticity is applied to formulate the stresses, strains, glottal tissue impedance, and propagation characteristics for sinusoidal oscillation within the vocal‐fold tissues. Incompressibility of the tissues leads to a biharmonic differential equation, the solution of which represents commonly observed modes of vibration. The energy dissipated in the tissues and the associated damping factors are calculated. Mode impedances of the tissues are calculated and lumped‐model approximations of the system evaluated. The usual mass‐spring models are shown to be inadequate in certain important cases, especially during vocal‐fold closure and for modes in which vertical phase differences occur. Subject Classification: [43]70.20.