Abstract: First principles theoretical study of the elastic and thermodynamic properties of erbium dihydride in fluorite structure, such as volume, thermal expansion, bulk modulus and isochoric heat capacity at different temperatures and pressures is performed using the plane wave pseudopotential method and the quasi-harmonic Debye model. The calculated isochoric heat capacity is convergent to the Dulong-Petit limit at temperatures over 1 100 K. The calculated lattice parameter of 0.523 2 nm at 0 GPa, and 0 K is in excellent agreement with the experimental value of 0.523 0 nm. Simultaneously, the data of single point energy versus volume of primitive cell are also calculated. According to the calculated values of the elastic constants at high pressures and the mechanical stability criteria of cubic crystals, the phase transition pressure is inferred to be about 20 GPa, which is a valid theoretical reference value for further experimental work in high pressure research.