Trapping effects that include significant delays in permeation saturation, abrupt changes in permeation rate associated with temperature changes, and larger than expected inventories of hydrogen isotopes in the material, were seen in implantation-driven permeation experiments using 25-µm and 50-µm thick tungsten foils at temperatures of 638–825 K. Computer models that simulate permeation transients reproduce the steady-state permeation and reemission behavior of these experiments with expected values of material parameters. However, the transient time characteristics were not successfully simulated without the assumption of traps of substantial trap energy and concentration. An analytical model based on the assumptions of thermodynamic equilibrium between trapped hydrogen atoms and a comparatively low mobile atom concentration successfully accounts for the observed behavior. Using steady-state and transient permeation data from experiments at different temperatures, the effective trap binding energy may be inferred. We analyze a tungsten coated divertor plate design representative of those proposed for ITER and ARIES and consider the implications for tritium permeation and retention if the same trapping we observed was present in that tungsten. Inventory increases of several orders of magnitude may result.