The results of experimental investigations at the initial stage of subnanosecond gas discharges [1] have been so far theoretically reasoned in the assumption that the sites of field emission, which takes place before explosive electron emission are geometric irregularities (micropoints and microprotrusions), which are generally present on a metal cathode. In work [2] it is shown that a substantial part in the processes occurring at the initial stage of subnanosecond gas discharges can be played by the microirregularities that have formed on the cathode as a result of absorption of atoms or molecules of the surrounding gas. In this case, for calculating the tunnel current density j the classical Fowler-Nordheim formula is used:formulaHere 0 2 y e eE ϕ πε = , e is the elementary charge, E is the electric field strength, h is Plank’s constant, ϕ is the work function of the cathode (considering the presence of the dialectical film), m is the mass of an electron, t(y) and v(y) are dimensionless tabulated functions, ε 0 is the permittivity of vacuum. The t(y) function is approximately equal to unity, and the v(y) function is defined in terms of elliptic integrals E1(k) and E2(k) of the first and second kind respectively. According to [3] (1 )   formula   . (2) Where a = (1−δ )2 − y2 , 0 4 * eEx δ ε = . (3) ε ∗ is the dielectric capacity of the adsorbed film which can acquire values in the range from 1 to value ε of the bulk sample. We have deduced a simple approximation formula v ( ó) ≈ 1.05 −1.27 ó3 2 . (4) Then, with an error of no more than 5 %, we can calculate the logarithm of the current intensity of prebreakdown electronic emission 2 3 2 1 4 lg j 6.15 lg E 31.09 37.81 E E ϕ ϕ ϕ = + − + . (5) Thus, the presence of tunnel absorbed nonmetallic layers or insular films on the picosecond cathode requires the following correction in the classical Fowler-Nordheim formula – the tunnel current density can increase (due to the reduction of v( y) ) or decrease (affected by he increased ϕ ). [1] G.A. Mesyats. Pis'ma v Zh. Eksper. Teoret. Fiz. 85 (2007) 119-122. [2] Yu. A. Barengolts. Tech. Phys. Lett. 38 (2012) 218-220. [3] S.I. Beril, E.P. Goryachkovskii, E.P. Pokatilov et al. Phys. Stat. Sol.(b) 176 (1993) 347-353.