Methane is a potent greenhouse gas, but its effects on Earth's climate remain poorly constrained, in part due to uncertainties in global methane fluxes to the atmosphere. An important source of atmospheric methane is the methane generated in organic-rich sediments underlying surface water bodies, including lakes, wetlands, and the ocean. The fraction of the methane that reaches the atmosphere depends critically on the mode and spatiotemporal characteristics of free-gas venting from the underlying sediments. Here we propose that methane transport in lake sediments is controlled by dynamic conduits, which dilate and release gas as the falling hydrostatic pressure reduces the effective stress below the tensile strength of the sediments. We test our model against a four-month record of hydrostatic load and methane flux in Upper Mystic Lake, Mass., USA, and show that it captures the complex episodicity of methane ebullition. Our quantitative conceptualization opens the door to integrated modeling of methane transport to constrain global methane release from lakes and other shallow-water, organic-rich sediment systems, and to assess its climate feedbacks.