Earlier particle experiments in the 1970s on Pioneer-10 and -11 and Voyager-1 and -2 provided Jupiter flyby particle data, which were used by Divine and Garrett to develop the first Jupiter trapped radiation environment model. This model was used to establish a baseline radiation effects design limit for the Galileo onboard electronics. Recently, Garrett et al. have developed an updated Galileo Interim Radiation Environment (GIRE) model based on Galileo electron data. In this paper, the GIRE model was utilized to generate trapped proton and electron spectra as a function of Rj (Rj = radius of Jupiter = ∼71,400 km). Using these spectra and a high-energy particle transport codes (MCNPX and HZETRN), radiation exposures and dose effects for a variety of shielding materials (Al, polyethylene [PE], and Ta plus several other elemental materials for “Graded-Z” portion of the paper) and thicknesses are presented for the Icy Moon, Europa, Ganymede, and Callisto for several orbital inclinations. In addition, an in-depth discussion and absorbed dose calculations are presented for “Graded-Z” materials and several computer codes were utilized for comparison purposes. We find overall there is generally quite good agreement between the various computer codes utilized in the study: MCNPX (Monte Carlo) vs. HZETRN (deterministic) for slab shielding and the comparison of “Graded-Z” shielding using the CEPXS, NOVICE, and NASA JPL codes. Finally, we conclude that the merits of using “Graded-Z” materials that include PE, due to cost and weight, should aid future Jupiter mission planners and spacecraft designers.