The beta-delayed emission process of gamma rays was treated with a gross theory of beta decay and a cascade gamma transition model. The method proposed was applied to calculations of the delayed gamma-ray energy spectra for short-lived fission product nuclides that lack experimental information on their gamma-ray transition properties. The calculated results were used to complement the summation calculation of the aggregate gamma-ray spectrum from an irradiated sample of fissile material after a short cooling time. A satisfactory agreement was obtained between the calculated and the measured spectra, which supported the appropriateness of the coupled gross beta and cascade gamma model. The method was also applied to the calculation of the equilibrium energy spectrum of the delayed gamma rays in operating reactors. The resulting shape resembles the prompt fission-gamma-ray spectrum.