Three-dimensional heat and mass transfer and electrochemical reaction in an anode-supported flat-tube solid oxide fuel cell (FT-SOFC) are studied. Transport and reaction phenomena mainly change in the streamwise direction. Exceptionally, hydrogen and water vapor have large concentration gradients also in the cross section perpendicular to the flow direction, because of the insufficient mass diffusion in the porous anode. Based on these results, we develop a simplified one-dimensional cell model. The distributions of temperature, current, and overpotential predicted by this model show good agreement with those obtained by the full three-dimensional simulation. We also investigate the effects of pore size, porosity and configuration of the anode on the cell performance. Extensive parametric studies reveal that, for a fixed three-phase boundary (TPB) length, rough material grains are preferable to obtain higher output voltage. In addition, when the cell has a thin anode with narrow ribs, drastic increase in the volumetric power density can be achieved with small voltage drop.