Transmission line surge arresters (TLAs) are vital elements for protection of power networks against the lightning surges. The proper selection of TLAs leads to a reduction of the lightning-related outages as well as the costs imposed to the power utility, because of the undelivered energy and damage to the equipment. The selection of the optimal arrester depends on how well its stresses can be estimated. Although a ground flash very frequently consists of multiple strokes, it is usual to consider only a single lightning stroke to calculate the lightning-related failures. A probabilistic method is presented for risk calculation that considers multiple strokes of each lightning flash to estimate the annual outage rate of TLAs. In the presented method, once the equivalent wave of the flash is computed, the probability of arrester failure is estimated by means of two indices, including total charge and maximum energy stress by the flash, separately. The energy stress caused by the flash is calculated using a few electromagnetic transient program (EMTP) simulations. Then, the obtained results from EMTP simulation are utilised to estimate the probability of failure. The accurate evaluation of failure probability of arresters permits the power utility to select the optimal arresters, considering a desirable average life.