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The Geant4-based PLANETOCOSMICS radiation simulation code has been extended to simulate the radiation environment in the vicinity of the Galilean moons. This software model treats in 3-dimensions the complex trajectories traced by charged particles in the combined effects of Jupiter's and the moon's intrinsic and induced fields. Furthermore, once the particles are incident upon the moon's surface, the detailed nuclear and electromagnetic interactions are modeled and secondary particle emission treated. Treatment of these complex processes allows more accurate prediction required for radiation environment and hardness assurance for future missions to these moons. This paper describes the basis of the PLANETOCOSMICS-J model and the simulation approach for the Galilean moons. The first results from applying the model to Europa are presented and show potentially 60-75% reduction in total ionizing dose for 500 km to 100 km circular orbits around the moon.