Abstract: The formation energy of all kinds of point defects formed by hydrogen or helium and the change of elastic constants of tungsten containing a point defect were studied by using first-principles method based on GGA with a PBE form. The other two kinds of point defects, such as vacancy and self interstitial atom in tungsten, were studied by using the same method. After calculation, we found that the crystal volume has some changes due to the formation of a point defect in the tungsten formed by hydrogen or helium. And the results depend on the sites of point defects. The crystal volume becomes bigger when the defects are located in the tetrahedron or octahedron sites, while the volume becomes smaller when a tungsten atom is replaced by a hydrogen or helium atom. For helium, the substitution site is the most favorable over the tetrahedron and octahedron sites. For hydrogen, on the contrary, the tetrahedron site is the most perfect site over the substitution and octahedron sites. In these defects, we can find the smallest formation energy corresponds to the defect formed hydrogen which located in tetrahedron site, and the biggest formation energy to the formation of a self interstitial atom. If tungsten contains a point defect formed by hydrogen or helium, the body modulus and the shear modulus will have some changes. The crystal will change to plastic when there is a hydrogen substitute defect or self interstitial atom in tungsten. The tungsten becomes more brittle when it contains other point defects, but it still has the ductility in total. The crystals may become anisotropy when there is a defect in tungsten, and the results depend on the site of the defects. Only for the defects at the substitute site, the anisotropy will not happen. The research  can provide a theoretical reference for the development of the plasma facing materials.