Stochastic Testing(ST) method is an uncertainty quantification method. The existing ST methods are still unable to handle situations with arbitrarily distributed variables. This paper uses the Gram-Schmidt orthogonalization algorithm to construct a chaotic polynomial basis for arbitrarily distributed random variables to extend ST method. The extended ST method is applied to the field line coupling analysis of transmission lines. In the calculation of field line coupling, due to the uncertainty of the radiation field, there is uncertainty in the polarization angle, azimuth angle, and elevation angle of the incident wave, resulting in uncertainty in the response of the transmission line, leading to the problem of random field line coupling. For the case where the input parameters follow an arbitrary distribution, ST method is applied to quantify the uncertainty of the coupling response of the transmission line field. Performing polynomial chaos expansion on the output response of the model and solving the expansion coefficients, statistical information of the model response is obtained. Combining the field line coupling examples of single random variable and multi-random variable, the statistical information of transmission line voltage response is obtained. Compared with Monte Carlo Simulation(MCS) method, the correctness and efficiency of the ST method are verified.