  In this paper we study the reconfinement of initially freely-expanding
unmagnetised relativistic jets by the pressure of non-uniform external gas
using numerical approach. The results are compared with the simple
semi-analytic model proposed by Komissarov & Falle (1997). In particular, we
explore the reconfinement in power-law atmospheres and in the King atmosphere,
which describes the X-ray coronas of giant elliptic galaxies. The results show
significant deviations from the KF model, which systematically underestimates
the reconfinement scale. For the power-law atmospheres the disagreement
increases with the power index k, exceeding two orders of magnitude for k=1.5.
For the King model, strong deviations are found on the outskirts of the
atmosphere, where the distribution approaches a power law. However for jets
reconfined inside the core, the reconfinement scale is increased only by the
factor of two. When the King model is modified by adding a central cusp, this
has little impact on the jets which are reconfined outside of the cusp region
but inside the cusp the reconfinement scale significantly reduces.
