Abstract:  To determin the analytical solutions of electromagnetic field and wave in and out of two-wire transmission lines transmitting analog signal，electromagnetic field and wave in and out of two-wire transmission lines is analysed and calculated based on maxwell equation from the angle of TEM wave，TM wave and TE wave in this paper.The results show that TM wave is transmitted in and out of two-wire transmission lines. The analytical solutions of electromagnetic field and wave in two-wire transmission lines consist of zero and 1st-order complex variable bessel functions，the analytical solutions of electromagnetic field and wave out of two-wire transmission lines consist of zero-order complex variable bessel functions and 1st-order complex variable Neumann functions，the relationship between electromagnetic field coefficient and electric current is given in this paper.The results further support for fitting calculation，simulation，signal distortion，electromagnetic compatibility analysing.

Key words: Two-wire transmission lines, Electromagnetic field and wave, Maxwell equations, Complex variable bessel functions, Analytic calculation