We have measured the vibrational modes of the sound producing membrane in the syrinx of zebra finches and canaries. Excised syringes were driven with a frequency-swept acoustic pressure wave through the trachea, and the resulting vibrations measured using a laser interferometer. The frequency-dependent membrane compliance was measured at 10-20 different positions, giving a detailed picture of the linear vibrational modes of the two membrane components, the medial labium and the medial tympaniform membrane. Nonlinear properties of the membrane were determined by measuring the linear response at several superimposed static pressures. The membrane compliance is dominated by the lowest vibrational mode, a narrow mechanical resonance, at roughly 700 Hz in the zebra finch, that extends over the entire membrane. Several higher-frequency modes were also observed. The frequency of the lowest vibrational mode is determined largely by the mass of the heavier medial labium, rather than the thinner medial tympaniform membrane, suggesting that the medial labium is critical in determining the oscillatory frequency of the syrinx. The difference in mass of the medial labium and medial tympaniform membrane may serve to produce a wave-like motion of the membranes during flow-driven oscillations, thus increasing the efficiency of sound production. Implications for mechanisms of frequency tuning are discussed.