Monoclinic　NaAsSe2　(γ-NaAsSe2)　has　been　reported　to　be　a　potential　IR　nonlinear　optical　material　due　to　the　very　strong　second　harmonic　generation　(SHG).　Here,　we　present　a　systematic　density　functional　theory　(DFT)　study　on　the　elasticity,　SHG　response,　linear　electro-optical　(EO)　effect,　and　piezoelectricity　of　this　compound　and　analyze　the　microscopic　origins　of　these　properties.　We　find　that　γ-NaAsSe　2　has　smaller　values　of　elastic　moduli　than　those　of　AgGaSe　2,　and　behaves　in　a　ductile　manner.　The　strong　SHG　response　observed　experimentally　is　well　predicted　by　the　2n　+　1　theorem　and　the　＇sum　over　states＇　expressions　based　on　the　DFT.　As　with　the　strong　SHG　response,　γ-NaAsSe2　also　presents　large　linear　EO　coefficient　(r　11　=　32.7　pm/V,　as　large　as　that　of　LiNbO3),　and　piezoelectric　coefficient　(e11　=　1.27　C/m2,　about　seven　times　larger　than　that　of　α-quartz).　The　highly　distorted　structure　and　the　strong　hybridizations　between　As　and　Se　sp　orbitals　are　identified　as　the　chief　sources　of　these　unique　properties.　Our　results　demonstrate　the　potential　applications　of　γ-NaAsSe2　in　piezoelectric,　electro-optical,　and　nonlinear　optical　devices.　©　2013　Elsevier　B.V.　All　rights　reserved.