The relationship between mechanical stress states and interfacial electrochemical thermodynamics of Li metal/Li6.5La3Zr1.5Ta0.5O12 and Na metal/Na-β”-Al2O3 systems are examined in two experimental configurations with an applied uniaxial load; the solid electrolytes were pellets and the metal electrodes high-aspect-ratio electrodes. Our experimental results demonstrate that (1) the change in equilibrium potential at the metal/electrolyte interface, when stress is applied to the metal electrode, is linearly proportional to the molar volume of the metal electrode, and (2) the mechanical stress in the electrolyte has negligible effect on the equilibrium potential for an experimental setup in which the electrolyte is stressed and the electrode is left unstressed. Solid mechanics modeling of a metal electrode on a solid electrolyte pellet indicates that pressure and normal stress are within ~0.5 MPa of each other for the high aspect ratio (~1:100 thickness:diameter in our study) Li metal electrodes under loads that exceed yield conditions. To assess the effect of electrochemical-mechanical coupling on current distributions at Li/single-ion conducting solid ceramic electrolyte interfaces containing a parameterized interfacial geometric asperity, we develop a coupled electrochemical-mechanical model and carefully distinguish between the thermodynamic and kinetic effects of interfacial mechanics on the current distribution. We find that with an elastic-perfectly plastic model for Li metal, and experimentally relevant mechanical initial and boundary conditions, the stress variations along the interface for experimentally relevant stack pressures and interfacial geometries are small (e.g., <1 MPa), resulting in a small or negligible influence of the interfacial mechanical state on the interfacial current distribution for both plating and stripping. However, we find that the current distribution is sensitive to interface geometry, with sharper (i.e., smaller tip radius of curvature) asperities experiencing greater current focusing. In addition, the effect on the current distribution of an identically sized lithium peak vs. valley geometry is not the same. These interfacial geometry effects may lead to void formation on both stripping and plating and at both Li peaks and valleys. This work advances the quantitative understanding of alkali metal dendrite formation within incipient cracks and their subsequent growth, and pore formation upon stripping, both situations where properly accounting for the impact of mechanical state on the equilibrium potential can be of critical importance for calculating the current distribution. The presence of high-curvature interface geometry asperities provides an additional perspective on the superior cycling performance of flat, film-based separators (e.g., sputtered LiPON) versus particle-based separators (e.g., polycrystalline LLZO) in some conditions.