In "real" metal-hydrogen systems the reacting metal (which is exposed to hydrogen at a given pressure and temperature) is initially coated by a thin passivation layer (referred to as an "oxide"). The initial penetration of hydrogen through this surface layer into the metal is a complex process consisting of different possible elementary steps. The nucleation of a hydride phase at the oxide-metal interface region initiates when the local concentration of hydrogen exceeds a certain solubility limit value. In the present work model calculations of the hydrogen concentration build-up at the oxide-metal interface were performed. In these calculations the permeation of hydrogen through the oxide was treated on a microscopic-atomic level, considering dissociative H2 chemisorption on the surface, atomic hydrogen jumps between adjacent oxide atomic layers and hydrogen transitions across the oxide-metal interface. The respective set of coupled differential equations was solved numerically, yielding the corresponding hydrogen penetration flux across the interface. The subsequent diffusion process of hydrogen into the metal was treated on a macroscopic level, solving numerically a diffusion equation for a semi-infinite medium. These calculations yielded the time required for the build-up of the limiting concentration value (at the interface region), i. e. the so-called "nucleation induction period", as a function of the different dynamic parameters involved in the process (e.g.) H2 sticking probabilities, hydrogen jump rate constants and hydrogen diffusion constants in the metal). A detailed analysis of surface-related parameters and diffusion parameter effects is presented. The results are applied to account for the qualitative trends observed in the initial nucleation and growth stages of some metal-hydrogen reactions.