Polystyrene foams have been generated and fabricated into differently shaped structures', by change of steaming period under constant impregnation time and solvent-nonsolvent composition. Optical photomicrographs of samples both plain and wax-copper-coated reveal uniform appearance, distinct grain-boundaries, and random cell size distribution. Dielectric measurements have been made on test specimens cut according to wave-guide size at 9.375 GHz X-band microwave frequency by short-circuited wave-guide method of Smith and Hippel modified by Dakin and Works. Dielectric constants are linear, on direct and semi-log scales in bulk-density and volume-fraction, obeying Weiner's inequalities. Formulae of Landau-Lifshitz, Beer, Maxwell-Wagner, Odelevsky, etc. have been tried. Data fit best with the logarithmic law of Lichtenecker and Rother. Specific polarization is also a true function of density. Dielectric constant vs bulk-density plots of foams resemble dielectric-constant vs fractional-density plots based on the theoretical derivation by Smith for polystyrene compacts, signifying that compacts containing closely-spaced oblong-spherical particles arc physically similar to foams having spherical gas inclusions in plastic structures. Tan δ lying in the range 0.002–0.0038 results from conformational polarization (β-relaxation at room-temperature for wide-angle torsional oscillations of side-groups with co-operative motion from wriggling chains). It is therefore possible for low-loss foam dielectrics suitable for micro-wave applications to be made by this method.