Abstract: An approximate solution of TEM wave in a parallel plate-cylindrical flat line is obtained by using the comformal mapping method. First,the cross section of parallel plate-cylindrical fiat line is transformed into the cross section of circular coaxial line by the conformal mapping,the solution of the electric field of the static field is obtained under the boundary conditions,and then the solution of the electric eield of TEM wave is got by multiplying the fluctuation factor. The magnetic field distribution is pressnted by the relationship of the contact of electirc and magnetic field accoding to the Maxwell＇ s equations,so the distribution of TEM wave in the circular coaxial line is given, and finally the distribution of TEM wave in the parallel plate-cylindrical fiat line is obtained by transformation function. By using Matlab softwave the map of the electromagnetic field the structure of TEM wave in the cross-section of the parallel plate-cylindrical fiat line is plotted, and its characteristic impedance is calculated. This research can be used to calculate the decay constant of the transnission line,realize its power capability,consider its power coupling and design the related active device.

Key words: conformal transformation, parallel plate-cylindrical flat line, TEM wave, characterstic impedance