A 3D convection-diffusion-reaction model was developed to describe CO oxidation in a continuous-flow catalytic reactor containing a Pd(100) single crystal surface. The model was studied with the help of the pseudo-arclength continuation algorithm, which is based on a matrix-free Newton–Krylov method and enables a one-parameter continuation of stationary solutions of large systems. The model was used to simulate the 3D spatial distributions of CO and CO2 during “light-off” experiments and the oscillations in CO oxidation over Pd(100) detected by the planar laser-induced fluorescence (PLIF) method. With realistic values of parameters the developed model can reproduce almost quantitatively the experimental reaction rates and the PLIF images measured under steady-state conditions and during self-sustained oscillations under near-atmospheric pressure conditions. The formation of a boundary layer and the essential decrease of CO concentration near the Pd(100) single crystal surface were demonstrated after the catalytic ignition and in a high activity branch of the oscillatory cycle indicating the mass-transfer limited regime.