Elastic properties of three high pressure polymorphs of CaCO3 are investigated based on first principles calculations.The calculations are conducted at 0 GPa-40 GPa for aragonite,40 GPa-65 GPa for post-aragonite,and 65 GPa-150 GPa for the P21/c-h-CaCO3 structure,respectively.By fitting the third-order Birch-Maghan equation of state (EOS),thevalues of bulk modulus K0 and pressure derivative K0’are 66.09 GPa and 4.64 for aragonite,81.93 GPa and 4.49 forpost-aragonite,and 56.55 GPa and 5.40 for P21/c-h-CaCO3,respectively,which are in good agreement with previous experimental and theoretical data.Elastic constants,wave velocities,and wave velocity anisotropies of the three highpressure CaCO3 phases are obtained.Post-aragonite exhibits 25.90％-32.10％ VP anisotropy and 74.34％-104.30％ Vs splitting anisotropy,and P21/c-h-CaCO3 shows 22.30％-25.40％ VP anisotropy and 42.81％-48.00％ VS splitting anisotropy in the calculated pressure range.Compared with major minerals of the lower mantle,CaCO3 high pressure polymorphs have low isotropic wave velocity and high wave velocity anisotropies.These results are important for understanding the deep carbon cycle and seismic wave velocity structure in the lower mantle.