The dynamic operation of a monolithic reactor was studied for the case of a planar crossflow solid oxide fuel cell (SOFC) monolith. A two-dimensional non-steady-state heterogeneous model was applied to a theoretical investigation of the electrochemical oxidation of H-2 in SOFCs monolithic arrangements, operating under forced periodic reversal of the flow. The present study shows the feasibility of this dynamic reactor operation mode, for the autothermal and highly efficient SOFC operation, also comparing the basic operational characteristics of the crossflow and co current flow SOFC arrangements. Results are reported on the dynamic evolution along the reactor of, fuel conversion, temperature and current distribution, thermodynamic energy conversion efficiency and volumetric power density. In fact, the successful application of this dynamic mode of operation can be proved to be of very high potential technological importance for the simple and highly efficient operation of an SOFC.