  Magnetohydrodynamical simulations are presented of a magnetized pulsar wind
interacting directly with the interstellar medium, or, in the case of a
surrounding supernova remnant, with the associated freely expanding ejecta of
the progenitor star. In both cases the simulations show that the pulsar wind
nebula will be elongated due to the dynamical influence of the toroidal
magnetic fields, which confirm predictions from a semi-analytical model
presented by Begelman & Li. The simulations follow the expansion of the pulsar
wind nebula when the latter is bounded by a strong shock and show that the
expansion can be modeled with a standard power-law expansion rate. By
performing different simulations with different magnetization parameters, I
show that the latter weakly correlates with the elongation of the pulsar wind
nebula. The results from the simulations are applied to determine the nature of
the expansion rate of the pulsar wind nebula 3C58. It is shown that there is
both observational and theoretical evidence which supports the scenario in
which the pulsar wind nebula 3C58 has caught up with the reverse shock of the
associated (but undetected) supernova remnant.
