Different compaction processes of the nanosized granular system, which is a prototype of an alumina nanopowder, are studied by the granular dynamics method. For all processes: compaction curves “density vs. pressure” of the powder compact are calculated, the elastic and the plastic parts are extracted from the total deformation, the body elastic moduli are determined within the isotropic solid approximation. The inadequacy of the isotropy approximation is established. The nanopowder yield surface is constructed in the space of stress tensor invariants. The inapplicability of the traditional associated flow rule for description of oxide nanopowders compaction processes is revealed. An alternative flow rule is suggested.