The cosmic-ray particles represent the valuable source of information about different celestial objects. Bombarding the bodies of the Solar System not protected with the atmosphere, they cause the generation of cosmogenic nuclides. Studying the production rates of cosmogenic nuclides in bodies, it is possible to derive important information about these bodies such as shielding capabilities, exposition time in the Solar System, dimensions or in case of meteorites also the time from the fall on the Earth. In our contribution, we would like to present our model for the simulation of the interaction of the primary galactic cosmic-ray protons with bodies. The model is based on Monte Carlo simulation software Geant4. The spherical body with predefined dimension, chemical composition and density is simulated which is bombarded by galactic protons with energies distributed according to the used energy spectrum. Within the spherical body the concentric shells with decreasing radius are considered which define the region where the fluxes of secondary protons and neutrons are calculated. In order to calculate the production rates of nuclides, the separate set of cross sections were used. The model calculates the production rates for selected cosmogenic nuclides.