In this paper, the eigen-function weighted boundary integral equation method (EW-BIEM) is applied to analyze the dispersion characteristics of various planar transmission lines with finite metallization thickness, such as the microstrip lines, conductor-backed coplanar waveguides and microcoplanar striplines for the first time. Due to the choice of the eigen-functions as weighted functions instead of Green's function, the computational time is shortened to a great extent and the singularity problems are also avoided. The difficulty in treating strip thickness can be overcome by considering the 90-degrees edge on the strip as a 90-degrees circular arc whose radius tends to zero. The computational results clearly demonstrate that the effects of finite strip thickness on the propagation properties of these transmission lines can be treated easily and efficiently with this method.