A method for stabilizing a cavity at a production or injection zone in an underground well includes providing a filtering element in the well at the cavity that is to be stabilized. The filtering element is formed with openings. The method further includes injecting a first fluid including expandable particles through the filtering element into the cavity. The expandable particles have a non-expanded state with a diameter smaller than the diameter of the openings of the filtering element. The method further includes injecting a second fluid through the filtering element. The second fluid is configured to react with the expandable particles such that the expandable particles expand to a diameter larger than the diameter of the openings in the filtering element, whereby the expanded particles and the filtering element form a filter at the production or injection zone in the well.