The elastic and thermodynamic properties of CsCl-type structure CaB 6 under high pressure are investigated by first-principles calculations based on plane-wave pseudopotential density functional theory method within the generalized gradient approximation (GGA). The calculated lattice parameters of CaB 6 under zero pressure and zero temperature are in good agreement with the existing experimental data and other theoretical data. The pressure dependences of the elastic constants, bulk modulus B (GPa), and its pressure derivative B′, shear modulus G, Young's modulus E, elastic Debye temperature Θ B , Zener's anisotropy parameter A, Poisson ratios σ, and Kleinmann parameter ζ are also presented. An analysis for the calculated elastic constants has been made to reveal the mechanical stability of CaB 6 up to 100GPa. The thermodynamic properties of the CsCl-type structure CaB 6 are predicted using the quasi-harmonic Debye model. The pressure–volume-temperature (P–V–T) relationship, the variations of the heat capacity C V , Debye temperature Θ D , and the thermal expansion α with pressure P and temperature T, as well as the Grüneisen parameters γ are obtained systematically in the ranges of 0–100GPa and 0–2000K.