The work is concerned with the numerical analysis of kinetics and thermodynamics of lithium insertion into electrode materials. The two methods for simulating diffusion in electrode material are shown. The Nernst-Planck flux formula and the law of mass conservation were chosen as the governing equations in a variable diffusivity model (VDM). These equations were solved for the planar electrode and for the different initial and boundary value conditions by means of the finite difference method. The distribution of lithium in the electrode material and the change of the Li+/LiyM half-cell potential are computed. The VDM is compared with a constant diffusivity model (CDM), the results confirm that dependence of the chemical diffusivity of Li on thermodynamics in binary system, M-LiyM, cannot be neglected in practical computations. (C) 2004 Elsevier B.V. All rights reserved.