The behavior of self-organizing granular medium in its own gravitational field is considered. The study is led within an approach proposing the existence of only three types of mesoscopic states in the material: so named hydrostatic, columnar and arched mesoscopic states. The results of this study are not obvious. Indeed, in the center of granular gravitating ball, as it turns out, pressure may be absent, though it is well-known that the pressure in either non-compressible liquid or solid linear-elastic medium is maximal. Such an uncommon stress state takes place at the arched mesoscopic state. Using the Mohr-Coulomb condition has given that the arched state can embody when sinus of internal friction’s angle increases up to the threshold value 1/3. At the hydrostatic mesoscopic state granular medium is like a liquid. The study also has shown the transition between hydrostatic and non-hydrostatic stress states being sharp in granular gravitating ball that opposes the known results of the linear theory of elasticity. At the columnar mesoscopic state any gravitating granular ball cannot be.