Soft X-ray emission has been observed from the low-latitude "disk" of both Jupiter and Saturn as well as from the auroral regions of these planets. The disk emission as observed by ROSAT, the Chandra X-Ray Observatory, and XMM-Newton appears to be uniformly distributed across the disk and to be correlated with solar activity. These characteristics suggest that the disk X rays are produced by (1) the elastic scattering of solar X rays by atmospheric neutrals and (2) the absorption of solar X rays in the carbon K-shell followed by fluorescent emission. The carbon atoms are found in methane molecules located below the homopause. In this paper we present the results of calculations of the scattering albedo for soft X rays. We also show the calculated X-ray intensity for a range of atmospheric abundances for Jupiter and Saturn and for a number of solar irradiance spectra. The model calculations are compared with recent X-ray observations of Jupiter and Saturn. We conclude that the emission of soft X rays from the disks of Jupiter and Saturn can be largely explained by the scattering and fluorescence of solar soft X rays. We suggest that measured X-ray intensities from the disk regions of Jupiter and Saturn can be used to constrain both the absolute intensity and the spectrum of solar X rays.