This paper reports a phase-field modeling (PFM) study of lithium (Li) electrodeposition process in Li‒metal battery (LMB) to explain its physics and morphology. Three regimes are investigated: Li filaments evolution, Li bush-like structure evolution and the transition between Li filaments and bush-like morphologies. The model takes into consideration the effect of solid electrolyte interface (SEI) on Li electrodeposits evolution. Also, an important new element of the model is the capability to represent the directional diffusion of Li by implementing diffusion tensor of Li-ions in the electrolyte, thus, allowing to simulate Li filaments root growth. In addition, an elastic deformation energy of the Li solid phase is included in the free energy functional of the PFM, which allows for monitoring the stress field and its influence on Li filaments/bush-like structure evolution. In particular, a significant stress is observed at the root of the Li electrodeposits, which can support the development of the experimental strategies to suppress their formation by lowering the stress field. Thus, the present study, in addition to improving the fidelity of the PFM of Li electrodeposition, identifies critical regimes of Li filaments growth and splitting, allowing for a more profound understanding of their influence on battery performance.