  Static and inflating brane world models are considered in $4+n$-dimensions
with a non zero bulk cosmological constant and with a hyper-spherically
symmetric topological defect residing in the $n$ extra dimensions. Several
vacuum solutions can be constructed explicitely when the bulk and inflating
constants are non zero. We study how these solutions are deformed by the
presence of a global monopole for generic values of $n$ and a local monopole
for $n=3$. New types of solutions, regular and periodic in the radial variable
relative to the extra dimensions, are constructed.
