Continuum-level mass and electronic transport through solid oxide cell electrodes, inclusive of ribbed interconnects, are modeled employing analytical solutions of the 2D Laplace equation. These analytical solutions describe localized mass and electronic transport phenomena in solid oxide fuel cell (SOFC) anodes and localized mass transport phenomena in SOFC cathodes. Two-dimensional constriction resistance effects created by reductions in active transport area are shown to significantly increase internal cell resistances by increasing transport path lengths within a cross-sectional region of the cell. Furthermore, these effects can alter cell performance with respect to fuel depletion phenomena and create a competition of losses between mass and electronic transport resistances. Fuel depletion is shown to occur at a current density lower than the traditionally defined limiting current density. An analytical expression for this fuel depletion current density is proposed based upon the models developed. The competition between mass transfer and electronic resistance effects arising from solid oxide cell interconnect geometry is also characterized through parametric studies based on a design of experiments (DOEs) approach. These studies demonstrate the benefits of smaller SOFC unit cell geometry.