HfO2 films are deposited by electron beam evaporation at a deposition rate of 0.03 nm/s and deposition temperature of 200 ℃ on K9 glass substrates. The films are observed to show a mixed structure of monoclinic and orthorhombic phase through X-ray diffraction and monoclinic phase is of obvious advantages. The structure parameters a, b, c and angel β of monoclinic HfO2 films are obtained using Jade5 software, based on which the crystal structure model is built. While solid crystal monoclinic HfO2 model is built to compare with the thin film one. Elastic stiffness constants of monoclinic HfO2 thin film and solid crystal are investigated using the plane waves ultrasoft pseudopotential technique based on the density functional theory (DFT) under two different exchange correlation functions of local density approximation (LDA) CA-PZ and generalized gradient approximation (GGA) PBE. Reuss, Voigt and Hill theories are used to estimate the bulk, shear and average Young′s moduli and Possion ratio for polycrystalline HfO2 thin film and solid crystal. In addition, the Young′s moduli in different orientations are also calculated.