Lanthanum　zirconate　(La2Zr2O7,　or　LZ)　has　been　widely　recognized　as　a　promising　candidate　material　for　thermal　barrier　coating　(TBC)　applications　since　it　has　low　thermal　conductivity,　high-temperature　phase　stability,　and　low　sintering　activity.　However,　the　mechanical　properties　of　LZ　crystal　have　not　been　fully　understood,　which　hinders　it　from　future　applications.　In　this　work,　atomistic　simulations　were　performed　to　study　the　anisotropic　mechanical　properties　of　LZ　crystal.　Using　both　the　first　principles　and　molecular　dynamics　(MD)　calculations,　uniaxial　tensile　tests　of　LZ　crystal　in　[001],　[011],　and　[111]　directions　were　simulated.　The　stress-strain　curves　of　the　tensile　tests　were　calculated,　and　the　ultimate　tensile　strength　and　toughness　were　derived.　The　Young＇s　moduli　in　[001],　[011],　and　[111]　directions　were　calculated　using　both　the　stress-strain　curves　and　an　analytical　method　for　small　deformation.　Additionally,　shear　stress-strain　curves　in　{111}＜　110　＞　and　{111}＜　11　(2)　over　bar　＞　directions　were　investigated　using　both　the　first　principles　calculations　and　the　MD　method.　Results　show　that　Young＇s　modulus　of　LZ　crystal　is　highly　anisotropic.　The　crystal　has　the　highest　Young＇s　modulus　in　[111]　direction,　and　{111}＜　11　(2)　over　bar　＞　direction　is　the　favorable　slip　system　during　shear　deformations.