Solid-state lithium metal batteries require accommodation of electrochemically generated mechanical stress inside the lithium: this stress can be1,2 up to 1 gigapascal for an overpotential of 135 millivolts. Maintaining the mechanical and electrochemical stability of the solid structure despite physical contact with moving corrosive lithium metal is a demanding requirement. Using in situ transmission electron microscopy, we investigated the deposition and stripping of metallic lithium or sodium held within a large number of parallel hollow tubules made of a mixed ionic-electronic conductor (MIEC). Here we show that these alkali metals—as single crystals—can grow out of and retract inside the tubules via mainly diffusional Coble creep along the MIEC/metal phase boundary. Unlike solid electrolytes, many MIECs are electrochemically stable in contact with lithium (that is, there is a direct tie-line to metallic lithium on the equilibrium phase diagram), so this Coble creep mechanism can effectively relieve stress, maintain electronic and ionic contacts, eliminate solid-electrolyte interphase debris, and allow the reversible deposition/stripping of lithium across a distance of 10 micrometres for 100 cycles. A centimetre-wide full cell—consisting of approximately 1010 MIEC cylinders/solid electrolyte/LiFePO 4 —shows a high capacity of about 164 milliampere hours per gram of LiFePO 4 , and almost no degradation for over 50 cycles, starting with a 1× excess of Li. Modelling shows that the design is insensitive to MIEC material choice with channels about 100 nanometres wide and 10–100 micrometres deep. The behaviour of lithium metal within the MIEC channels suggests that the chemical and mechanical stability issues with the metal–electrolyte interface in solid-state lithium metal batteries can be overcome using this architecture.