The dynamic faradic properties of the lithium ion batteries are primarily determined by the process of lithium ion insertion into a porous electrode. In this paper, we present an analytical result of the intercalating process of Li/Li+ into a spherical particle of graphite or cobalt oxide immersed in a conductive electrolyte. Using the finite integral transform method, an exact solution to the concentration profile was obtained for arbitrary linear initial and boundary conditions. To avoid analytical difficulties with respect to the boundary conditions of second kind, the method of pseudo-steady-state is applied. The final solution uniformly converges, and can be used for accurate and fast dynamic modelling and simulation. (c) 2005 Elsevier B.V. All rights reserved.