The production of molecular hydrogen in the radiolysis of high-density polyethylene, isotactic polypropylene (PP), poly(methyl-methacrylate) (PMMA), and polystyrene (PS) by gamma rays and 5-20-MeV helium ions was investigated. Molecular hydrogen is the dominant gaseous product from these polymers, and the yields with gamma rays are 3.3, 2.6, 0.24, and 0.033 molecules per 100 eV of energy absorbed for polyethylene, PP, PMMA, and PS, respectively. The decrease in observed hydrogen is due to increased branching and the chemical nature of the groups on the side chains. There is an increase in hydrogen production with increasing linear energy transfer (LET) from gamma rays to helium ions, but the relative increase depends on the polymer type. With incident 5-MeV helium ions, the respective yields of molecular hydrogen are 4.6, 3.2, 0.62, and 0.15 molecules per 100 eV. The increase in molecular hydrogen with increasing LET may be due to changes in the kinetics of hydrogen precursors in the particle tracks. The differences in the relative increases in molecular hydrogen with increasing LET for each of the polymers suggests that self-scavenging reactions may be important for low LET particles.