  X-ray observations of extragalactic radiosources show strong evidences of
interaction between the radio emitting plasma and the X-ray emitting ambient
gas. In this paper we perform a detailed study of this interaction by numerical
simulations. We study the propagation of an axisymmetric supersonic jet in an
isothermal King atmosphere and we analyze the evolution of the resulting X-ray
properties and their dependence on the jet physical parameters. We show the
existence of two distinct and observationally different regimes of interaction,
with strong and weak shocks. In the first case shells of enhanced X-ray
emission are to be expected, while in the second case we expect deficit of
X-ray emission coincident with the cocoon. By a comparison between analytical
models and the results of our numerical simulations, we discuss the dependence
of the transition between these two regimes on the jet parameters and we find
that the mean controlling quantity results to be the jet kinetic power. We then
discuss how the observed jets can be used to constrain the jet properties.
