  We construct a regular five-dimensional brane-world with localised gravity on
a flat 3-brane. The matter content in the bulk is parametrised by an analog of
a non-linear fluid with equation of state $p=\gamma\rho^\lambda$ between the
`pressure' $p$ and the `density' $\rho$ dependent on the 5th dimension. For
$\gamma$ negative and $\lambda>1$, the null energy condition is satisfied, and
the geometry is free of singularities within finite distance from the brane,
while the induced four-dimensional Planck mass is finite.
