The paper presents the results of experimental investigation of energy and flux dependences of hydrogen isotopes and oxygen trapping in carbon materials (carbon fiber composite and pyrolitic graphite), and metals (stainless steel and nickel) under irradiation in the deuterium gas discharge plasma with and without oxygen addition. The dependence of hydrogen trapping on ion energy, ion current density, oxygen addition in deuterium plasma are presented and analyzed. The sorbed molecules, containing hydrogen atoms from the residual gas and deuterium atoms of the working gas are shown to be the important source of hydrogen trapping in both carbon based materials and stainless steel. Irradiation of the SS vacuum vessel with the neutrals or/and ions of (D2+O2) plasma initiate the hydrogen diffusion from the vessel wall and H2, HD, D2O, HDO, H2O molecule formation on the wall surface. Trapping of the low energy plasma particles and the particles from the sorbed molecules as well as modification of working gas composition are considered as the processes provided at the expense of the potential energy of plasma particles with respect to the surface and occurred through their inelastic collisions with the surface. The hydrogen trapping occurred due to “potential” processes was named as “potential”, and in contrast the trapping of fast particles due to their kinetic energy was labeled as “kinetic”.