It has been reported that running a Solid Oxide Electrolysis Cell above a critical current degrades the cell very quickly. This degradation has been linked to oxygen bubble formation in the electrolyte near the oxygen electrode. The applied current in the presence of charge transfer resistances is responsible for a high oxygen potential under the oxygen electrode which translates into a large driving force for the formation of oxygen gas in the electrolyte and can lead to the nucleation of oxygen gas bubbles. When such a bubble nucleates, local equilibrium at the interface between the bubble and oxide leads to an extremely high pressure inside it introducing, in return, significant stresses in the oxide. In this paper, the stress field surrounding the oxygen bubbles in the electrolyte is treated and the resulting elastic energy is determined.