Solid-state lithium metal batteries require accommodation of electrochemically generated mechanical stress inside the lithium: this stress can be(1,2) 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 10(10) MIEC cylinders/solid electrolyte/LiFePO4-shows a high capacity of about 164 milliampere hours per gram of LiFePO4, and almost no degradation for over 50 cycles, starting with a 1x 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. By containing lithium metal within oriented tubes of a mixed ionic-electronic conductor, a 3D anode for lithium metal batteries is produced that overcomes chemomechanical stability issues at the electrolyte interface.