The radial density distributions of the positive column of stmngly modulated low -pressure gas discharges in mercury-rare gas mixtures at 10 tom pressure have been studied theoretically. The current was modulated sinusoidally with a modulation depth of 50%. Calculations have shown that the radial profile of the excited atoms is ditferent form 0th Bessel function J0(2.4r/R) and the invertion of the radial distribution of the excited atom can occur at some frequency. The hybrid method of FDM and 2nd order Runge-Kutta meth od is used for solving differenzial equations,