Hardness is defined as a phenomenological measure of resistance of a material to shear stresses under local volume compression. It is shown that this definition may serve as a theoretical basis for existing empirical relationships between the Vickers microhardness H-V and the various phenomenological, packing density-sensitive parameters of non-crystalline materials, including among them, the internal pressure, the glass transition temperature T-g, the excess enthalpy, and the free volume fraction at T-g.