Battery technology plays an important role in energy storage. In particular, lithium-ion (Li-ion) batteries are of great interest, because of their high capacity, long cycle life, and high energy and power density. However, for further improvements of Li-ion batteries, a deeper understanding of physical processes occurring within this type of battery, including transport, is needed. To provide a detailed description of these phenomena, a 3D representation is required for the morphology of composite materials used in Li-ion batteries. In this paper, we develop a stochastic simulation model in 3D, which is based on random marked point processes, to reconstruct real and generate virtual morphologies. For this purpose, a statistical technique to fit the model to 3D image data gained by X-ray tomography is developed. Finally, we validate the model by comparing real and simulated data using image characteristics which are especially relevant with respect to transport properties. (C) 2011 Elsevier B.V. All rights reserved.