We offer an explanation for how dendrite growth can be inhibited when Li metal pouch cells are subjected to external loads, even for cells using soft, thin separators. We develop a contact mechanics model for tracking Li surface and sub-surface stresses where electrodes have realistically (micron-scale) rough surfaces. Existing models examine a single, micron-scale Li metal protrusion under a fixed local current density that presses more or less conformally against a separator or stiff electrolyte. At the larger, sub-mm scales studied here, contact between the Li metal and the separator is heterogeneous and far from conformal for surfaces with realistic roughness: the load is carried at just the tallest asperities, where stresses reach tens of MPa, while most of the Li surface feels no force at all. Yet, dendrite growth is suppressed over the entire Li surface. To explain this dendrite suppression, our electrochemical/mechanics model suggests that Li avoids plating at the tips of growing Li dendrites if there is sufficient local stress; that local contact stresses there may be high enough to close separator pores so that incremental Li+ ions plate elsewhere; and that creep ensures that Li protrusions are gradually flattened. These mechanisms cannot be captured by single-dendrite-scale analyses. (C) The Author(s) 2019. Published by ECS.