Different modifications of the method of linear integral representation are studied. Solutions of the related inverse problems based upon a “gibrid version of two approximations” of the topography and geopotential fields enable more refined tuning of the method in solving the inverse problems of geophysics and geomorphology and more complete allowance for the a priori information about the surface elevation data and elements of anom- alous fields. The technique for finding a stable approximate solution for the inverse problem of determining the mass distributions equivalent by the external gravitational (or any other potential) field is presented. The method is applied to study anomalous densities beneath one of the highest elevation Elysium Mons and deep Hellas basin on Mars. The results of the mathemati- cal experiment are discussed.