The modeling of neodymium ions extraction from the mixture of D2EHPA and TOPO by the hollow fiber supported liquid membrane has been studied. The system is operated in an once-through-mode and H2SO4 is used as stripping solution. Mathematical models have been developed based on a fluid-flow model including the term of axial convection, axial diffusion, chemical reaction at the feed-liquid membrane and accumulation of neodymium ions. The models are solved by a finite difference method on the MATLAB software.