We investigated the mode of growth of flat-topped mud volcanoes, through the study of three active edifices onshore Azerbaijan: they are the Bozdag-Guzdek, the Ayazakhtarma and the Akhtarma-Pashaly mud volcanoes. The three edifices are up to 80 m high and 3 km wide, and the recurrence time between eruptions from a few months to a few years. Surface changes during and between eruptions were documented by a combination of mapping from satellite pictures, repeated direct observation over five years and structural analysis. In addition, resistivity profiles and microgravity measurements were used to decipher their subsurface geometries. We interpret the flat-topped character of the mud volcanoes as the result of rapid “isostatic” readjustment of a brittle surface crust, < 1 m to tens of meters thick, overlying a ductile layer. The surface structure typically shows a concentric transition from an extensional regime in the vicinity of the emission center, to strike slip movements in a median ring, to a compressional regime with thrusts, and pop-up blocks or folds in the outer part of the plateau. Both the flat surface of these mud volcanoes and observed radial displacements of the surface, combined with the very low Bouguer anomaly of the Ayazakhtarma mud volcano, give arguments to propose that km-diameter, flat-topped mud volcanoes likely reflect the presence at a shallow depth (a few tens of meters?) of a large volume of soft mud. Rapid compaction at the surface forms a crust that moves away from a central feeding area, thereby transferring mud added at the center into lateral spreading, building a Coulomb prism all around the mud volcano and strongly limiting vertical buildup.