  Boxy/peanut (b/p) bulges, the vertically extended inner parts of bars, are
ubiquitous in barred galaxies in the local Universe, including our own Milky
Way. At the same time, a majority of external galaxies and the Milky Way also
possess a thick-disc. However, the dynamical effect of thick-discs in the b/p
formation and evolution is not fully understood. Here, we investigate the
effect of thick-discs in the formation and evolution of b/ps by using a suite
of N-body models of (kinematically cold) thin and (kinematically hot) thick
discs. Within the suite of models, we systematically vary the mass fraction of
the thick disc, and the thin-to-thick disc scale length ratio. The b/ps form in
almost all our models via a vertical buckling instability, even in the presence
of a massive thick disc. The thin disc b/p is much stronger than the thick disc
b/p. With increasing thick disc mass fraction, the final b/p structure gets
progressively weaker in strength and larger in extent. Furthermore, the
time-interval between the bar formation and the onset of buckling instability
gets progressively shorter with increasing thick-disc mass fraction. The
breaking and restoration of the vertical symmetry (during and after the b/p
formation) show a spatial variation -- the inner bar region restores vertical
symmetry rather quickly (after the buckling) while in the outer bar region, the
vertical asymmetry persists long after the buckling happens. Our findings also
predict that at higher redshifts, when discs are thought to be thicker, b/ps
would have more 'boxy-shaped' appearance than more 'X-shaped' appearance. This
remains to be tested from future observations at higher redshifts.
