A model is presented for the differential fluxes of galactic cosmic ray (GCR) particles with energies above 1 MeV inside any spherical stony meteorite as a function of the meteorite's preatmospheric radius and the samples's depth. This model is based on the Reedy-Arnold equations for the energy-dependent fluxes of GCR particles in the moon and is an extension of flux parameters that were derived for several meteorites of various sizes. This flux model is used to calculate the production rates of many cosmogenic nuclides as a function of radius and depth. The peak production rates for most nuclides that are created by the reactions of energetic GCR particles occur near the centers of meteorites with radii of 40 to 70 g cm-2. The calculated production rates usually agree well with measurements of cosmogenic nuclides in most meteorites. Although the model has some limitations, it reproduces well the basic trends observed for the depth-dependent production of cosmogenic nuclides in stony meteorites of various radii. Some of these production profiles are different from those of other calculations. The chemical dependence of the production rates for several nuclides varies with size and depth.