Originally demonstrated with electromagnetic waves, supercoupling describes the extraordinary matched transmission, energy squeezing, and anomalous quasistatic tunneling through narrow channels. This behavior is the result of impedance matching achieved when the effective properties within the channel approach zero. For electromagnetic waves, supercoupling is observed when the electric permittivity in the channel approaches zero. These channels are accordingly known as epsilon-near-zero (ENZ) channels. This work shows that analogous behavior exists in the acoustic domain when the effective density is nearly zero, which can be achieved by tailoring the structure of the channel. Such channels are therefore known as density-near-zero (DNZ) metamaterial channels. Unlike tunneling based on Fabry-Perot resonances, DNZ transmission is independent of channel length and geometry and yields a uniform field along the entire length of the channel. Transmission-line theory is used to describe this peculiar phenomenon and finite element simulations are presented to confirm the unusual transmission properties of the metamaterial channel. It is further shown that acoustic waves may provide a unique possibility of squeezing acoustic energy through arbitrarily small channels in three dimensions, overcoming limitations that arise in the electromagnetic case.