We build upon the concept that nucleation of lithium dendrites at the lithium anode-solid state electrolyte interface is instigated by the higher resistance of grain boundaries that raises the local electro-chemical potential of lithium, near the lithium-electrode. This excess electro-chemo-mechanical potential, however, is reduced by the mechanical back stress generated when the dendrite is formed within the electrolyte. These parameters are coalesced into an analytical model that prescribes a specific criterion for dendrite formation. The results are presented in the form of current limit diagrams that show the “safe” and “fail” regimes for battery function. A higher conductivity of the electrolyte can reduce dendrite formation.