This chapter discusses the major features of development of prompt radiation fields and the shielding of these fields as they are produced at proton and ion accelerators. It focuses on the shielding of neutrons in view of their general dominance of the radiation fields. The chapter provides the shielding against muons at such accelerators. It presents methods for utilizing the results of both semi-empirical and Monte Carlo methods in the solution of practical shielding problems. The ionization range of a proton increases monotonically with energy. Since the mass of the proton is so much larger than that of the electron, the radiative processes of bremsstrahlung and synchrotron radiation are usually negligible at proton accelerators. At proton accelerators muons arise from two principal mechanisms: from pion and kaon decay and from “direct” production. Direct muon production is important at only very high–energy proton accelerators.