Knowledge of the levels of tritium in the First Wall (FW) coolant and components of ITER is important for public and operator safety and waste management. To overcome the large uncertainty of plasma wall interaction and physical properties, a basic set of properties is theoretically calculated for the dissolved tritium atoms in a perfect Beryllium (Be) lattice. These properties are combined with models for tritium trapping by lattice imperfections including the equilibrium conditions between gaseous, dissolved and trapped hydrogen isotopes. The 3 models for trapping by impurities, radiation damage and surface defects are adjusted to experimental solubilities, to tritium release experiments from irradiated samples and to outgassing of hydrogen isotopes from the JET FW. An elastic lattice model evaluates the activation energy of diffusion. For the calculations, the code DIET (Diffusion, Implantation and Equilibrium Trapping) was developed, which includes tritium trapping with time-dependent trap concentrations of multiple trap sites. The sensitivity analysis, with the expected deviations from the basic properties provides confidence that tritium permeation is below one gram in ITER for a neutron load of 0.3 MWa/m2 within 10 years.