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Lithium (Li) dendrite formation in Li-metal batteries (LMBs) remains a key obstacle preventing LMBs from their widespread application. This study focuses on the role of the stress field in the Li electrodeposits formation and growth. Coupled electrochemical and mechanical phase-field model (PFM) is used to investigate electrodeposited Li evolution under different conditions. The PFM results, using both the anisotropic elastic properties of Li and the random delivery of Li-ions through the solid electrolyte interface, show a significant local stress development indicating a direct correlation between the stress field and the origin of the undesired Li filaments initiation.