  Recent HI observations reveal that the discs of spiral galaxies are
surrounded by extended gaseous haloes. This extra-planar gas reaches large
distances (several kpc) from the disc and shows peculiar kinematics (low
rotation and inflow). We have modelled the extra-planar gas as a continuous
flow of material from the disc of a spiral galaxy into its halo region. The
output of our models are pseudo-data cubes that can be directly compared to the
HI data. We have applied these models to two spiral galaxies (NGC891 and
NGC2403) known to have a substantial amount of extra-planar gas. Our models are
able to reproduce accurately the vertical distribution of extra-planar gas for
an energy input corresponding to a small fraction (<4%) of the energy released
by supernovae. However they fail in two important aspects: 1) they do not
reproduce the right gradient in rotation velocity; 2) they predict a general
outflow of the extra-planar gas, contrary to what is observed. We show that
neither of these difficulties can be removed if clouds are ionized and
invisible at 21cm as they leave the disc but become visible at some point on
their orbits. We speculate that these failures indicate the need for accreted
material from the IGM that could provide the low angular momentum and inflow
required.
