An oxidation process is simulated for a bundle of metal tubes in a cross–flow. The fluid flow is governed by the incompressible Navier–Stokes equations. To describe the transport of oxygen, the corresponding convection–diffusion equation is applied. The key point of the model is related to the description of oxidation processes, taking into account the growth of a thin oxide film in the quasi-stationary approximation. Mathematical modeling of oxidant transport in a tube bundle is carried out in the 2D approximation. The numerical algorithm employed in the work is based on the finite-element discretization in space and the Crank–Nicolson discretization in time. The tube rows of a bundle can be either in-line or staggered in the direction of the fluid flow velocity. The growth of the oxide film on tube walls is predicted for various bundle structures using the developed oxidation model. © 2018 Elsevier Inc.