  A possible mechanism for screening of the surface magnetic field of an
accreting neutron star, by the accreted material, is investigated. We model the
material flow in the surface layers of the star by an assumed 2-D velocity
field satisfying all the physical requirements. Using this model velocity we
find that, in the absence of magnetic buoyancy, the surface field is screened
(submergence of the field by advection) within the time scale of material flow
of the top layers. On the other hand, if magnetic buoyancy is present, the
screening happens over a time scale which is characteristic of the slower flow
of the deeper (hence, denser) layers. For accreting neutron stars, this longer
time scale turns out to be about $10^5$ years, which is of the similar order as
the accretion time scale of most massive X-ray binaries.
