We have performed theoretical investigations on the structure, equation of state (EOS), elasticity of the cubic ( space group of P4232, No: 208) and tetragonal ( space group of P42/nmcs, No: 137) Cd3As2 crystal by using the first-principles pseudopotential plane-wave method. The bulk modulus and its pressure derivation are obtained by fitting the energy–volume points to Birch–Murnaghan equation of state. Moreover, according to the Voigt–Reuss–Hill approximation, the elastic moduli of Cd3As2 are also successfully predicted. By employing the quasi-harmonic Debye model, the thermal expansion coefficient, bulk modulus, cell volume and heat capacity at different temperatures are also obtained.