A large number of polycrystalline and amorphous materials ranging from pure metals to glassy polymers have been found to obey the relations α2E=150 [dyn cm-2°K-2]s at normal temperatures. The linear coefficient of expansion is denoted by α, Young's modulus by E, and s is a dimensionless spread factor (0.5≪s≪2). The spread of about ±0.3 decade is small compared to the three‐decade range of E covered by the data. Notable exceptions to the relation are certain alloys, some inorganic glasses, cellular materials (e.g., wood), granular materials (e.g., cement), and rubbery materials. The variations with temperature of α, E, and heat capacity Cp are compared for representative materials and implications of the α2E relation are discussed. An empirical approach in which generalized Grüneisen numbers are utilized and a preliminary statistical mechanical attempt to relate α to Cv and the elastic properties of polymers are discussed. Both lead to the conclusion that for polymers, perhaps even more so than for metals, it would be of interest to make separate measurements to very low temperatures of α, Cp, and various elastic moduli.