The erosion module of the SOLPS 4.3 code package for the liquid Li divertor target is developed to include the thermal sputtering, evaporation, and prompt redeposition effects. Eroded Li atoms are treated within a fully kinetic approach. Simulations for the T-15MD tokamak with liquid Li divertor targets are performed for various operational regimes. The main parameters characterizing the divertor operation are identified. The Li shielding effect is found significant at the input power PSOL > 15 MW. The target conditions remain reasonable in terms of both the erosion rate and target temperature but core plasma dilution with Li remains a problem. The Li flow patterns in the scrape-of-layer (SOL) are analyzed in detail. About 80% of eroded Li is redeposited back on the target. The energy dissipated per an eroded Li particle, Esh, is calculated and its values are in the range of 100–200 eV. These values are 2–4 times lower than those obtained from a simple 0D estimation of Esh. Therefore, relying on simple 0D models for the analysis of Li divertor performance may cause an overestimation of the shielding efficiency.