Despite rapid damping, fish swimbladders have been modelled as underwater resonant bubbles. Recent data suggest that swimbladders of soundproducing fishes use a forced rather than a resonant response to produce sound. The reason for this discrepancy has not been formally addressed, and we demonstrate, for the first time, that the structure of the swimbladder wall will affect vibratory behaviour. Using the oyster toadfish Opsanus tau, we find regional differences in bladder thickness, directionality of collagen layers (anisotropic bladder wall structure), material properties that differ between circular and longitudinal directions (stress, strain and Young's modulus), high water content (80%) of the bladder wall and a 300-fold increase in the modulus of dried tissue. Therefore, the swimbladder wall is a viscoelastic structure that serves to damp vibrations and impart directionality, preventing the expression of resonance.