Abstract The spherically symmetric motion of a rarified gas of the explosive type, due to the instantaneous release of a finite mass of gas and the finite energy associated with it in an infinitely small volume, is studied. A kinetic model is proposed which is refined compared with that proposed by the authors for the corresponding one-dimensional motion. The asymptotic solution as t → 0 is studied (for the spherical and planar cases). A difference scheme is constructed and numerical investigations are carried out. The solutions obtained are compared with experimental data on the discharge of barium in the upper layers of the atmosphere and also with calculations using known gas dynamic models.