  We present the results of an extensive theoretical investigation on the
pulsation behavior of Bump Cepheids. We constructed several sequences of full
amplitude, nonlinear, convective models by adopting a chemical composition
typical of Large Magellanic Cloud (LMC) Cepheids (Y=0.25, Z=0.008) and stellar
masses ranging from 6.55 to 7.45 solar masses. We find that theoretical light
and velocity curves reproduce the HP, and indeed close to the blue edge the
bump is located along the descending branch, toward longer periods it crosses
at first the luminosity/velocity maximum and then it appears along the rising
branch. In particular, we find that the predicted period at the HP center is
11.24 +- 0.46 d and that such a value is in very good agreement with the
empirical value estimated by adopting the Fourier parameters of LMC Cepheid
light curves. We also find that the models at the HP center are located within
the resonance region but not on the 2:1 resonance line. Interestingly enough,
the predicted Bump Cepheid masses, based on a Mass-Luminosity (ML) relation
which neglects the convective core overshooting, are in good agreement with the
empirical masses of Galactic Cepheids estimated by adopting the Baade-Wesselink
method. Even by accounting for the metallicity difference between Galactic and
LMC Cepheids, this result seems to settle down the long-standing problem of the
Bump mass discrepancy. Finally, the dynamical behavior of a cool Bump Cepheid
model provides a plain explanation of an ill-understood empirical evidence.
