We carried out hydrostatic pressure demagnetization experiments up to 1.24GPa on samples of terrestrial and extraterrestrial rocks and minerals of different lithologies as well as on synthetic samples. The magnetic remanence of samples was measured directly under pressure using a non-magnetic high pressure cell of piston-cylinder type that was inserted into a high sensitivity SQUID magnetometer. In order to bring light on the pressure demagnetization effect, we investigated 50 samples with different magnetic mineralogies, remanent coercivities () and hysteresis parameters. The samples consisted of pyrrhotite-, magnetite- and titanomagnetite-bearing Martian meteorites, taenite-, tetrataenite and kamacite-bearing ordinary chondrites and pyrrhotite-bearing Rumuruti chondrite; magnetite- and titanomagnetite-bearing basalts, andesites, ignimbrites, obsidians and granites; a variety of pyrrhotite- and hematite-bearing rocks and minerals (jasper, schist, rhyolite, radiolarite); samples of goethite and greigite as well as synthetic samples of dispersed powders of magnetite, hematite, pyrrhotite and native iron set into epoxy resin. Under hydrostatic pressure of 1.24GPa, applied in a low magnetic field (<5μT), the samples lost up to 84% of their initial saturation isothermal remanent magnetization (SIRM) without any changes in their intrinsic magnetic properties. We found that the efficiency of the pressure demagnetization is not exclusively controlled by the magnetic hardness of the samples (), but that it is strongly dependent on their magnetic mineralogy. For a given magnetic mineralogy the resistance to hydrostatic pressure is roughly proportional to ln(). It was shown that there is no simple equivalence between pressure demagnetization and alternating field demagnetization effects. The pressure demagnetization was shown to be time-independent but repeated application of the same pressure level resulted in further demagnetization.