The statistical probability of flashover on high-voltage (HV) overhead lines is an important factor in ensuring the continuity of uninterrupted operation of the transmission line. The determination of the aforementioned probability is most often carried out using specialized software packages (ElectroMagnetic Transients Program, EMTP) and Monte Carlo simulations. This requires a very time-consuming calculation. This paper presents a new statistical method for calculating the probability of flashover, based on the use of EMTP, but without the need for Monte Carlo simulations. The proposed method, namely, separates the statistical distribution of lightning current parameters from the simulations of flashovers in the EMTP program, using the Gaussian copula and the curve of limiting parameters. In this way, the total number of numerical simulations required to determine the statistical distribution of the probability of flashover is reduced many times, because these are systematic and not stochastic simulations. At the same time, the application of the Gaussian copula allows the construction of a multivariate statistical distribution (lightning current incident on a line) by separately observing the structure of the correlation matrix from the marginal distributions. In this case, the marginal distribution of the amplitudes of the current incident on a line depends on its geometry, according to the electrogeometric model (EGM) of the development of a lightning strike on an overhead line.