© The Author(s) 2016. Understanding and controlling the electrochemical deposition of lithium is imperative for the safe use of rechargeable batteries with a lithium metal anode. Solid block copolymer electrolyte membranes are known to enhance the stability of lithium metal anodes by mechanically suppressing the formation of lithium protrusions during battery charging. Time-resolved hard X-ray microtomography was used to monitor the internal structure of a symmetric lithium-polymer cell during galvanostatic polarization. The microtomography images were used to determine the local rate of lithium deposition, i.e. local current density, in the vicinity of a lithium globule growing through the electrolyte. Measurements of electrolyte displacement enabled estimation of local stresses in the electrolyte. At early times, the current density was maximized at the globule tip, as expected from simple current distribution arguments. At later times, the current density was maximized at the globule perimeter. We show that this phenomenon is related to the local stress fields that arise as the electrolyte is deformed. The local current density, normalized for the radius of curvature, decreases with increasing compressive stresses at the lithium-polymer interface. To our knowledge, our study provides the first direct measurement showing the influence of local mechanical stresses on the deposition kinetics at lithium metal electrodes.