The mechanical properties of MH2 (M= La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc, Ti, Zr, Hf) are studied by the first-principles calculations. The results show that the fluorite structures of MH2 (M= La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc) are stable at low temperatures. Their bulk moduli, shear moduli and Young's moduli increase in the order of LaH2, NdH2, GdH2, TbH2, YH2, DyH2, HoH2, ErH2, LuH2 and ScH2. However, the cubic phases of MH2 (M= Ti, Zr, Hf) are unstable at low temperatures. According to the densities of states and charge densities of TbH2, ErH2, TiH2 and HfH2, it can be found that the stabilities of metal dihydrides depend on the interaction between metal and hydrogen atoms.