  A thin limit description of the 6D Cascading DGP model is derived, starting
from a configuration where both the codimension-1 and the codimension-2 branes
are thick. Postulating that the thicknesses of the two branes obey a hierarchic
relation, the thin limit is executed in two steps. First the thin limit of the
codimension-1 brane is executed, obtaining a system where a "ribbon"
codimension-2 brane is embedded inside a thin codimension-1 brane with induced
gravity, and then the thin limit of the ribbon brane is considered. By
proposing a geometric ansatz on the limit configuration, the junction
conditions which are to hold at the thin codimension-2 brane are derived. The
latters are fully non-perturbative and covariant and, together with the Israel
junction conditions at the codimension-1 brane and the Einstein equations in
the bulk, constitute the looked-for thin limit formulation of the 6D Cascading
DGP model. It is commented on how wide is the class of thin source
configurations which can be placed on the thin codimension-2 brane.
