Electrokinetic separations can be used to quickly separate rare earth metals to determine their forensic signature. In this work, we simulate the concentration and separation of trivalent lanthanide cations by isotachophoresis. A one-dimensional simulation is developed using COMSOL v4.0a, a commercial finite element simulator, to represent the isotachophoretic separation of three lanthanides: lanthanum, terbium, and lutetium. The binding ligand chosen for complexation with the lanthanides is alpha-hydroxyisobutyric acid (HIBA) and the buffer system includes acetate, which also complexes with the lanthanides. The complexes formed between the three lanthanides, HIBA, and acetate are all considered in the simulation. We observe that the presence of only lanthanide: HIBA complexes in a buffer system with 10 mM HIBA causes the slowest lanthanide peak (lutetium) to split from the other analytes. The addition of lanthanide: acetate complexes into the simulation of the same buffer system eliminates this splitting. Decreasing the concentration of HIBA in the buffer to 7 mM causes the analyte stack to migrate faster through the capillary.