We introduce the acoustic equivalent of “supercoupling” by studying the anomalous sound transmission and uniform energy squeezing through ultranarrow acoustic channels filled with zero-density metamaterials. As a realistic example, we propose their realization by inserting transverse membranes with a subwavelength period along the channel, and we prove a novel form of acoustic tunneling based on impedance matching and infinite phase velocity at the zero-density operation. We envision applications in sensing, noise control, cloaking, and energy harvesting.