The　influence　of　the　existing　site　preference　of　the　constituent　elements　on　the　sublattice　on　elastic　properties　is　rarely　explored　in　multi-principal　element　alloys　(MPEAs).　In　this　work,　in　order　to　explore　the　influence　of　the　site　preference　of　constituent　atoms　on　the　thermodynamic　properties　and　elastic　properties,　the　ordered　configurations　based　on　the　previously　predicted　site　occupying　fractions　(SOFs)　and　the　disordered　configuration　based　on　a　special　quasi-random　structure　(SQS)　were　established,　and　the　thermodynamic　properties　and　elastic　properties　were　predicted　using　the　quasi-harmonic　approximation　(QHA)　method　first.　It　was　found　that　the　site　preferring　behaviors　of　atoms　on　the　sublattices　will　not　only　improve　the　stability　of　the　structure　but　will　also　lead　to　bigger　elastic　properties　than　its　ideal　disordered　structure.　Although　the　prediction　of　the　temperaturedependent　elastic　properties　using　the　QHA　method　shortens　the　time　costs　by　only　considering　the　effects　of　thermal　expansion,　it　ignores　the　significant　effect　of　lattice　vibration　on　elastic　properties　at　high　temperatures.　In　order　to　explore　the　influence　of　lattice　vibration　on　the　temperature-dependent　elastic　properties　further,　the　elastic　properties　of　the　ordered　FCC_CoCrFeNi　MPEA　were　predicted　using　the　ab　initio　molecular　dynamics　(AIMD)　method　at　several　selective　temperatures.　The　results　show　that　except　for　the　elastic　constant　C12　and　bulk　modulus,　the　lattice　vibration　reduces　other　elastic　properties　on　the　basis　of　thermal　expansion.　The　predicted　temperature-dependent　shear　and　Young＇s　moduli　agree　well　with　the　limited　experimental　literature　data.　Thus,　the　temperature-dependent　elastic　properties　can　be　reasonably　predicted　using　the　AIMD　method　based　on　site　preference.　The　predicted　polycrystalline　elastic　moduli　B,　G,　and　E　of　FCC_CoCrFeNi　MPEA　at　973　K　are　146.68,　53.79,　and　143.78　GPa,　respectively.