Abstract: During the process of constructing an ideal electromagnetic invisibility cloak with expanding mapping method, a singularity problem which leads to extreme parameters on the inner boundary, is inevitable and could cause a serious impact on both practical implementation and working bandwidth of such cloaking devices. In this paper, three different types of processing ways are summarized to deal with this singularity problem, among which the second type of method is specifically analyzed with detailed parameter diagrams and numerical simulation results to prove its validity.