A solid oxide fuel cell comprises a porous anode electrode, a dense non-porous electrolyte and a porous cathode electrode. The anode electrode comprises a first member and a plurality of parallel plate members extending from the first member. The cathode electrode comprises a second member and a plurality of parallel plate members extending from the second member. The plate members of the cathode electrode inter-digitate with the plate members of the anode electrode and the electrolyte fills the spaces between the first and second members and the parallel plate members of the anode electrode and the cathode electrode.