The paper deals with the gas dynamic approach to describing processes that cause the formation of a leader – area of significant non-uniform charge concentration. As a result a strong electric field is formed initiating the atmospheric gas break-down. The solution for a set of nonlinear equations of weakly ionized gas is found in one-dimensional case and the concentration distributions for particles and electric field in the gas flow are obtained. The initial conditions of the problem determine to a great degree the regimes of initial distribution instability of charged particles concentration; the fields of parameter changes are investigated, when the electrical field increase leads to the discontinuity lines similar to shockwaves in gases but with the compression of electrical nature. The numerical solutions for the set of equations are obtained without any of the previously used approximations. It is demonstrated that the electrical field and non-uniform concentration distribution increase significantly in the hydrodynamic flow, however, the field remains finite within the established time-space limits of a thunderstorm charged cloud.