The invention relates to monitoring of fluid-filled domains in various media including, for example, subterranean formations, construction elements, bones. Claimed are a method for determining characteristic sizes of a fluid-filled crack in a medium and a system for implementation thereof. In accordance with this method, oscillations of the fluid-filled crack are registered. Wave characteristics of standing interface waves propagating along the fluid-filled crack surfaces are determined based on the registered oscillations taking medium and fluid properties into account. The fluid-filled crack characteristic sizes are calculated based on the determined wave characteristics of the standing interface waves. Also claimed are methods for detecting creation or existence of a fluid-filled crack in a medium, for hydraulic fracturing in a subterranean formation, for detecting cessation of propagation of a fluid-filled crack in a medium, as well as a method for determining properties of a fluid filling a layer in a medium, of the medium and of the layer. Analysis of oscillations of fluid-filled domains based on interface waves propagating along their surfaces underlies all the methods listed above. The proposed methods, by virtue of the simplicity of data processing inherent thereto, can be implemented in real time.