The elastic stiffness coefficients of single crystal AlLi with cubic NaTl (B32) structure were calculated at 0 K from the first principles. The obtained elastic stiffness coefficients, in units of GPa, were c₁₁=66.9, c₁₂=38.2 and c₄₄=51.7. Then the bulk modulus, Young’s modulus, shear modulus and Poison’s ratio were estimated for polycrystalline AlLi from the elastic stiffness coefficients. The Young’s modulus for single crystal AlLi was the highest in the ⟨111⟩ direction. The formation of the sp³-like bond connecting the nearest-neighbor Al atoms was confirmed from the charge density distribution. The elastic anisotropy of AlLi was compared with those of the sp³ bonded semiconductors such as Si and GaAs.