  Cosmological N-body simulations indicate that the dark matter haloes of
galaxies should be generally triaxial. Yet, the presence of a baryonic disc is
believed to alter the shape of the haloes. Here we aim to study how bar
formation is affected by halo triaxiality and how, in turn, the presence of the
bar influences the shape of the halo. We perform a set of collisionless N-body
simulations of disc galaxies with triaxial dark matter haloes, using elliptical
discs as initial conditions. We study models of different halo triaxialities
and, to investigate the behaviour of the halo shape in the absence of bar
formation, we run models with different disc masses, halo concentrations, disc
velocity dispersions and also models where the disc shape is kept artificially
axisymmetric. We find that the introduction of a massive disc causes the halo
triaxiality to be partially diluted. Once the disc is fully grown, a strong
stellar bar develops within the halo that is still non-axisymmetric, causing it
to lose its remaining non-axisymmetry. In triaxial haloes in which the initial
conditions are such that a bar does not form, the halo is able to remain
triaxial and the circularisation of its shape on the plane of the disc is
limited to the period of disc growth. We conclude that part of the
circularisation of the halo is due to disc growth, but part must be attributed
to the formation of a bar. We find that initially circular discs respond
excessively to the triaxial potential and become highly elongated. They also
lose more angular momentum than the initially elliptical discs and thus form
stronger bars. Because of that, the circularisation that their bars induce on
their haloes is also more rapid. We also analyse halo vertical shapes and
observe that their vertical flattenings remain considerable, meaning that the
haloes become approximately oblate by the end of the simulations. [abridged]
