The difficulties in the interpretation of electrochemical data caused by a nonuniform current distribution at the electrode is a well-known problem of electrochemistry, e.g., see Ref. 1 and 2 for reviews. The nonuniform reaction rate may result from the particular cell geometry, including the placement of the reference electrode, from reaction kinetics, mass-transfer limitations, or a combination. Measured quantities such as ohmic and polarization resistance, and other knietic parameters can deviate considerably from their true values based on material and interfacial properties of the cell components. A mathematical model can thus be a useful tool to relate measured quantities to the true properties.In the field of solid-state electrochemistry, a nonlinear dependence of the ohmic resistance on the electrolyte thickness was observed in experiments with Au electrodes partly covering the surface of an yttria-stabilized zirconia (YSZ) electrolyte. 3,4 For porous electrodes, a discrepancy between the measured ohmic drop and the theoretical ohmic drop was reported for La 1Ϫx Sr x MnO 3 5 and Pt electrodes, 6 and attributed to a constriction of the current as a result of discrete contact points at the electrode/electrolyte interface. Simple and approximate analytical formulas were developed to relate the ohmic resistance to the geometry of the cell. 4-6 Furthermore, it is well established that the ac impedance of multicrystalline YSZ electrolyte exhibits an additional semicircle on a Nyquist plot in comparison to a single-crystal electrolyte, 7,8 and this is attributed to constriction of current lines caused by grain boundaries or defects. A rigorous, theoretical treatment of this problem was presented by Fleig and Maier 9,10 for a rectangular element with an electrode much smaller than the dimensions of the cell, under ac conditions. Nagata et al. 11 performed an experimental study of the effect of cell configuration and the position of the reference electrode on the measured potential, using YSZ electrolyte and Pt electrodes. The results were interpreted in terms of intuitive equivalent circuits. Figueiredo et al. 12 investigated two different cell geometries experimentally, with emphasis on the effect of the electrolyte thickness on the measured overpotential at an La 0.9 MnO 3 electrode/YSZ electrolyte interface. The potential distribution in a thin YSZ electrolyte was calculated numerically for a specific cell geometry. 13 Winkler et al. 14 evaluated solid electrolyte cell geometries with respect to possible errors in the determination of the polarization resistance by means of numerical analysis.This study gives a theoretical treatment of current and potential distributions in simple two-dimensional cell geometries representative of typical solid-state cells commonly used in the laboratory for the evaluation of reaction kinetics and properties of cell components. Emphasis is given to problems related to the use of thin electrolytes and the kinetic properties of the counter electrode, relevant for studies of solid...