There is currently a great amount work devoted to the development of electrodes for Li-ion batteries. Silicon is one of the most promising candidates, because it shows high charge capacity and low discharging rates. However, silicon experiences a huge volume expansion about 400% during the lithiation/delithiation process. As shown recently, silicon nano-wires are attractive candidates for electrodes because they provide less constraint on the volume changes that occur during Li charging. In the present study, we have tried to estimate the critical size below which fracture does not occur in silicon nano-wires.