Recent considerations by Wada make it appropriate to extend a previous discussion of Gru¨neisen ``numbers'' for polymers and other molecular solids. Wada hypothesized that the proper Gru¨neisen constant for polymers is&ggr;G=&agr;V/&bgr;Cvb, whereCvbis theinterchain contribution to the heat capacity at constant volume; &agr;, &bgr;, andVare the volumetric thermal expansivity, the compressibility, and the volume. To the extent that a polymer can be treated as a vibrational lattice, the hypothesis appears to be consistent with&ggr;G=&Sgr;&ggr;i&egr;(xi)/&Sgr;&egr;(xi), averaged over Einstein oscillator functions &egr;(xi) withxi=hvi/kT. At low temperatures, &egr;(xi) is much larger for the low‐frequency modes, so that they tend to determine &ggr;Gbelow the Debye −&thgr;. Since &ggr;i=−∂ ln&ngr;i/∂ lnVand since low &ngr;iare likely to be more sensitive to changes inV, it is expected that &ggr;Gwill be larger for molecular solids than for metallic, ionic, or covalent crystals. Earlier predictions and Wada's calculations agree that &ggr;G≈4 might be typical for polymers and suggest that ∂&ggr;/∂T>0. The correlation,E&agr;l2≈15 N/m2°K2, between modulusEand linear expansivity &agr;lled to the prediction, now verified, that there should be relations between the harmonic and anharmonic moduli. The anharmonic coefficients in the relation &Dgr;V/V0=a1p+a2p2+a3p3+&cellip;area2=C1a12anda3=C3a13, where for metalsC2=−2.5±0.5, and for polymersC2=−4.0±0.1 andC3=8.8±0.2. A phenomenological theory based on a ``bundle of tubes'' model is developed which is in good agreement with data and according to which &ggr;G=−C2andd&ggr;G/dT∼&agr;C2. The relation of &ggr;Gto intermolecular potential functions also is discussed and some qualtitatively encouraging results are obtained.