Geometry of crossing null shells

New geometric objects on null thin layers are introduced and their importance for crossing null-like shells are discussed. The Barrab`es–Israel equations are represented in a new geometric form and they split into decoupled system of equations for two different geometric objects: tensor density ${\mathbf{G}}^a{}_b$ and vector field $I$. Continuity properties of these objects through a crossing sphere are proved. In the case of spherical symmetry Dray–t’Hooft–Redmount formula results from continuity property of the corresponding object.