Compressibility of deep fluids-filled cavern is discussed. Compressibility is measured both through statical and dynamical tests. Statical compressibility is influenced by cavern shape and the nature of cavern fluids. This parameter plays an important role for such applications as the determination of stored hydrocarbons volume, of volume lost during a blow-out and of pressure build-up rate in a closed cavern. Dynamical compressibility is measured through the periods of waves triggered by pressure changes. Both tube waves and longer period waves associated to the existence of an interface between a liquid and a gas can be observed. They allow checking of the results of the statical tests and can provide additional information, for instance the existence of trapped gas in the well-head.