The compressibility, tensile strength, and mechanical resistance to shear of a solid are related to the corresponding moduli (bulk, Young’s, and shear modulus), which are derived from the coefficients of elasticity. First-principles calculations of these fundamental mechanical properties give values of the same quality as experimental data, but at a substantially smaller effort and cost. This is demonstrated here for cubic silicon carbide, β-SiC, corundum, α-Al₂O₃, and a tourmaline with a fairly complex crystal structure. First-principles calculations are a valuable source for these fundamental materials property data.