Abstract: A new analytical approach to the statistical theory of sonic boom propagation through randomly inhomogeneous media is developed on the base of nonlinear evolution equations. The turbulent atmosphere layer is modelled by a random phase screen. A new Burqers' type equation is derived for arbitrary speeds of supersonic aircrafts using nonlinear geometrical acoustics approximation. The average peak pressure, squared pressure and dispersion of fluctuations are calculated, as well as statistical distributions for peak pressure and its outbursts. It is shown that in spite of decrease in the main characteristics of the N-wave, the fluctuations can increase and lead to the appearance of undesirable outbursts.