Seeps found offshore in the East Siberian Arctic Shelf may mark zones of degrading subsea permafrost and related destabilization of gas hydrates. Sonar surveys provide an effective tool for mapping seabed methane fluxes and monitoring subsea Arctic permafrost seepage. The paper presents an overview of existing approaches to sonar estimation of methane bubble flux from the sea floor to the water column and a new method for quantifying CH4 ebullition. In the suggested method, the flux of methane bubbles is estimated from its response to insonification using the backscattering cross section. The method has demonstrated its efficiency in the case study of single- and multi-beam acoustic surveys of a large seep field on the Laptev Sea shelf.