The process of the lepton pair production by a neutrino propagating in an external electromagnetic field is investigated in the framework of the Standard Model. Relatively simple exact expression for the probability as the single integral is obtained, which is suitable for a quantitative analysis.Nowadays, it is well established that a medium makes an active influence on the quantum processes. It stimulates a constantly growing interest in the particle physics in medium, especially in view of possible astrophysical manifestations. It should be noted that a consideration of an intense electromagnetic field as the medium, along with a dense matter, is physically justified indeed. Really, the field strengths inside the astrophysical objects can reach the critical Schwinger value B e = m 2 e /e ≃ 4.41 · 10 13 G 1 , and even could exceed it essentially. On the other hand, the situation is possible when 1 We use natural units in which c = = 1.