At present accurate evaluation of the capacitances of transmission lines is desired. Most TEM mode transmission lines have cross-sections with reentrant corners where the potential gradient is singular. In this paper MEI is used with nonuniform grids to extract the capacitance parameter in the presence of reentrant corners. The mathematical model of electric field near the reentrant is given and its analytical solution formation is derived. Finite series expansion is used to approximate the analytical solution, and a novel method is proposed to calculate the charge of conductor. Compared with Duncan correction the technique avoids the choice of the integral length of normal derivative near the reentrant and it can be used with nonuniform grids more conveniently. The error analysis of asymptotic approximation of finite series expansion is also given. Numerical experiments are presented for analysis.