The motion with intersections of relativistic gravitating shells in the Schwarzschild gravitational field of a central body is considered. Formulas are derived for calculating parameters of the shells after intersection via their parameters before intersection. Such special casesas the Newtonian approximation, intersections of light shells, and intersections of a test shell with a gravitating shell are also considered.The ejection of one of the shells to infinity in the relativistic region is described. The equations of motion for the shells are analyzed numerically. Motion of two intersecting shells can shows a chaotic behaviour. For the case when one can neglected by influence of gravitation of one ("light") shell onto another ("heavy") shell ("restricted problem") the structure of the phase space is described and the scaling laws for the measure of the domain of chaotic motion and for the minimal energy of the light shell sufficient for escape to infinity are obtained.