Based on the studies on how the volume fraction of lithium particles (i.e., Li-C/Li-Si chemical compound) affects the elastic modulus of a battery electrode, a new mathematical approach, which considers the influence of lithium ions concentration and Li-C/Li-Si binding energy in electrodes, has been proposed for prediction of the effective elastic modulus of electrodes in this work. Firstly, 2-D battery models were built using COMSOL Multiphysics, which consist of graphite and silicon matrix electrodes, respectively. Secondly, the changes of lithium ions concentration and porosity of electrodes in graphite and silicon electrodes have been simulated and then the changes of lithium ions concentration and porosity of electrodes were obtained. Using those data, an analytical model had been constructed, which can consider the influence of particles volume fraction, lithium ions concentration and Li-C/Li-Si binding energy at the same time.