Solid-state batteries are arguably the most promising development in battery technology. However, commercialisation is hindered by the nucleation and growth of dendrites, needle-like structures between electrodes that short circuit the batteries. The nucleation of dendrites is a two-stage process. First, during stripping, voids form at the anode, adjacent to the electrode-electrolyte interface. Those voids lead to a reduction in the contact area between the electrode and the solid electrolyte and trigger the development of ‘hot-spots’, regions of high current that arise at void corners. Then, during plating, dendrites nucleate in those hot-spot regions. It has been recently hypothesised that applying a stack pressure can prevent voiding and consequently suppress dendrite formation. Thus, there is a need to develop electrochemo-mechanical models capable of predicting void evolution and the development of hot-spots as a function of the material, applied pressure and charge. In this work, we present the first phase field formulation for predicting void evolution in all-solid state batteries and conduct relevant numerical experiments on solid state batteries using Li metal as anode material. The phase field order parameter describes the evolution of the void-Li metal interface, as driven by the nucleation and annihilation of Li lattice sites. Creep effects are captured by using a viscoplastic formulation for Li, and the interplay between vacancy diffusion, oxidation and creep deformation is quantified as a function of the applied pressure and current. Moreover, the electrolyte current distribution is solved for and thus ‘hot-spots’ are predicted for electrode-electrolyte systems developing multiple voids and undergoing several stripping and plating cycles. We show that the model can capture the main trends observed in the experiments, bring complementary insight, and map safe regimes of operation.