Previous studies showed that chemical modified Bacillus subtilis biomass possessed the high potential for recovery rare-earth elements, and, in this study, mathematical models were applied to explain the B. subtilis biomass La3+ and Sm3+ ions sorption capacity. The experimental isotherm data were analyzed using Langmuir, Freundlich, Temkin, and DRK equations. Both Langmuir and Freundlich isotherms models that fit the equilibrium data. Temkin model showed that it occurs physisorption. In more dilute solutions, the adsorption preference follows the order La3+ > Sm3+. With the increase in the concentration of rare-earth elements, there is an inversion in the preference for Sm3+ > La3+. The results demonstrate that the optimum model for describing the kinetics of the biosorption of both rare-earth elements is the pseudo-second-order model as well as the viability of recovering lanthanum using bacterial biomass sorbents, a practical technique.