Particles and heavy ions are used in various fields of nuclear physics, medical physics, and material science, and their interactions with different media, including human tissue and critical organs, have therefore carefully been investigated both experimentally and theoretically since the 1930s. However, heavy-ion transport includes many complex processes and measurements for all possible systems, including critical organs, would be impractical or too expensive e.g. direct measurements of dose equivalents to critical organs in humans cannot be performed. A reliable and accurate particle and heavy-ion transport code is therefore an essential tool in the design study of accelerator facilities as well as for other various applications. Recently, new applications have also arisen within transmutation and reactor science, space and medicine, especially radiotherapy, and several accelerator facilities are operating or planned for construction. Accurate knowledge of the physics of interaction of particles and heavy ions is also necessary for estimating radiation damage to equipment used on space vehicles, to calculate the transport of the heavy ions in the galactic cosmic ray (GCR) through the interstellar medium, and the evolution of the heavier elements after the Big Bang. Concerns about the biological effect of space radiation and space dosimetry are increasing rapidly due to the perspective of long-duration astronaut missions, both in relation to the International Space Station and to manned interplanetary missions in near future. Radiation protection studies for crews of international flights at high altitude have also received considerable attention in recent years. There is therefore a need to develop accurate and reliable particle and heavy-ion transport codes. To be able to calculate complex geometries, including production and transport of protons, neutrons, and alpha particles, 3-dimensional transport using Monte Carlo (MC) technique must be used. Today several particle and heavy-ion MC transport codes exist, e.g. Particle and Heavy-Ion Transport code System (PHITS), High Energy Transport Code-Human Exploration and Development of Space (HETC-HEDS). SHIELD-HIT, GEANT4, FLUKA. MARS. and MCNPX. In this paper, we present an extensive benchmarking of the calculated projectile fragmentation cross-sections from the reactions of 300-1000MeV/u Si-28, Ar-40, and Fe-56 on polyethylene, carbon. aluminum. and copper targets (relevant to space radioprotection) using PHITS, FLUKA, HETC-HEDS, and MCNPX, against measurements. The influence of the different models used in the different transport codes on the calculated results is also discussed. Some measured cross-sections are also compared to the calculated cross-sections using NUCFRG2, which are incorporated in the 1-dimensional, deterministic radiation transport code HZETRN.