It is shown that the soliton solutions to generalized versions of the
Skyrme model with stabilizing terms of high order in the derivatives d
evelop a bag structure with well defined interior and exterior regions
. The equation of motion reduces to that of the non-linear sigma-model
in the exterior region when the order of the stabilizing terms become
s infinite. When the parameters of the model are chosen so that the nu
cleon and the DELTA33 masses are maintained at their empirical values
in taking the infinite order limit the ''bag'' radius is in the range
0.5-1.0 fm, the exact value depending on the combination of stabilizin
g terms.