Differential　stresses　are　expected　to　influence　the　properties　of　minerals.　The　structural　and　Raman　vibrational　properties　of　calcite　under　hydrostatic　and　differential　stresses　were　studied　using　a　first-principles　method　based　on　density　functional　theory.　Our　results　show　that　the　density　of　calcite　increases　or　decreases　under　different　differential　stress,　relative　to　its　value　under　hydrostatic　pressure.　The　calculated　effects　of　differential　stress　on　bond　lengths　are　nominal.　As　pressure　increases,　the　frequencies　of　all　Raman　modes　increase,　with　their　pressure　derivatives　slightly　depending　on　the　differential　stress.　The　state　of　stress　influences　the　Raman　modes　by　shifting　their　frequencies　to　either　higher　or　lower　values　relative　to　the　corresponding　hydrostatic　results.　In　particular,　the　largest　and　smallest　frequency　shifts　were　predicted　for　E-g-156　and　A(1g)-1086　modes,　respectively,　when　the　additional　stress　was　applied　along　the　a-axis.　Visualization　of　atomic　motions　associated　with　Raman　modes　suggests　that　the　differential　stress-induced　shifts　in　Raman　frequencies　are　controlled　by　out-of-plane　vibrations　of　atoms.　The　stress　estimated　on　the　basis　of　the　experimentally　measured　shift　of　the　Raman　frequency　of　calcite　sample　gathered　from　the　Wuchuan　earthquake　fault　by　applying　our　calculated　dv(iota),/dP　value　of　A(1g)-1085　mode　is　785　MPa,　which　appears　to　be　comparable　to　the　stress　inferred　at　the　Wuchuan　earthquake　focus.　Thus,　the　first-principles　simulations　and　Raman　spectroscopy　experiments　together　may　help　us　in　elucidating　the　state　of　stress　in　the　Earth＇s　interior.