  We show by numerical simulations that a purely stellar dynamical model
composed of an exponential disc, a cuspy bulge, and an NFW halo with parameters
relevant to the Milky Way Galaxy is subject to bar formation. Taking into
account the finite disc thickness, the bar formation can be explained by the
usual bar instability, in spite of the presence of an inner Lindblad resonance,
that is believed to damp any global modes. The effect of replacing the live
halo and bulge by a fixed external axisymmetric potential (rigid models) is
studied. It is shown that while the e-folding time of bar instability increases
significantly (from 250 to 500 Myr), the bar pattern speed remains almost the
same. For the latter, our average value of 55 km/s/kpc agrees with the
assumption that the Hercules stream in the solar neighbourhood is an imprint of
the bar--disc interaction at the outer Lindblad resonance of the bar. Vertical
averaging of the radial force in the central disc region comparable to the
characteristic scale length allows us to reproduce the bar pattern speed and
the growth rate of the rigid models, using normal mode analysis of linear
perturbation theory in a razor thin disc. The strong increase of the e-folding
time with decreasing disc mass predicted by the mode analysis suggests that
bars in galaxies similar to the Milky Way have formed only recently.
