  We present modelling of the $\beta\,$Cep star HD\,180642 based on its
observational properties deduced from CoRoT and ground-based photometry as well
as from time-resolved spectroscopy. We investigate whether present-day
state-of-the-art models are able to explain the full seismic behaviour of this
star, which has extended observational constraints for this type of pulsator.
We constructed a dedicated database of stellar models and their oscillation
modes tuned to fit the dominant radial mode frequency of HD\,180642, by means
of varying the hydrogen content, metallicity, mass, age, and core overshooting
parameter. We compared the seismic properties of these models with those
observed. We find models that are able to explain the numerous observed
oscillation properties of the star, for a narrow range in mass of
11.4--11.8\,M$_\odot$ and no or very mild overshooting (with up to 0.05 local
pressure scale heights), except for an excitation problem of the $\ell=3$,
p$_1$ mode. We deduce a rotation period of about 13\,d, which is fully
compatible with recent magnetic field measurements. The seismic models do not
support the earlier claim of solar-like oscillations in the star. We instead
ascribe the power excess at high frequency to non-linear resonant mode coupling
between the high-amplitude radial fundamental mode and several of the low-order
pressure modes. We report a discrepancy between the seismic and spectroscopic
gravity at the $2.5\sigma$ level.
