The physical description of the passage of heavy ions in tissue and shielding materials is of interest in radiobiology, cancer therapy and space exploration, including a human mission to Mars. Galactic cosmic rays (GCRs) consist of a large number of ion types and energies. Energy loss processes occur continuously along the path of heavy ions and are well described by the linear energy transfer (LET), straggling and multiple scattering algorithms. Nuclear interactions lead to much larger energy deposition than atomic-molecular collisions and alter the composition of heavy ion beams while producing secondary nuclei often in high multiplicity events. The major nuclear interaction processes of importance for describing heavy ion beams was reviewed, including nuclear fragmentation, elastic scattering and knockout-cascade processes. The quantum multiple scattering fragmentation model is shown to be in excellent agreement with available experimental data for nuclear fragmentation cross sections and is studied for application to thick target experiments. A new computer model, which was developed for the description of biophysical events from heavy ion beams at the NASA Space Radiation Laboratory (NSRL), called the GCR Event Risk-Based Model (GERMcode) is described.