Many barred galaxies, possibly including the Milky Way, have cusps in the centres. There is a widespread belief, however, that usual bar instability taking place in bulgeless galaxy models is impossible for the cuspy models, because of the presence of the inner Lindblad resonance for any pattern speed. At the same time there are numerical evidences that the bar instability can form a bar. We analyse this discrepancy, by accurate and diverse N-body simulations and using the calculation of normal modes. We show that bar formation in cuspy galaxies can be explained by taking into account the disc thickness. The exponential growth time is moderate for typical current disc masses (about 250 Myr), but considerably increases (factor 2 or more) upon substitution of the live halo and bulge with a rigid halo/bulge potential; meanwhile pattern speeds remain almost the same. Normal mode analysis with different disc mass favours a young bar hypothesis, according to which the bar instability saturated only recently.

8 pages, 5 figures