The mechanistic details of the hydrogen oxidation at Ni/YSZ anodes are subject of controversial discussion. In the light of potential accumulation of secondary phases at the three-phase boundary, a mechanism involving interstitial hydrogen species in the bulk phases and charge-transfer at the Ni/YSZ two-phase boundary has been proposed. We present a quantitative analysis of this mechanism based on a two-dimensional elementary kinetic model of electrochemistry and bulk diffusion. The use of literature diffusion coefficients yields diffusion-limited current densities that are below those observed in experiments. Assuming increased diffusivity allows to quantitatively reproduce published experimental pattern anode data, including their dependence on gas composition and temperature. This shows the feasibility of interstitial mechanisms when impurities are present and explains their decreased performance. For clean three-phase boundaries, surface spillover pathways are preferred.