Evolutionary tracks and pulsational analysis of models with masses of 13-18 M _ { \odot } are presented .
We address two important questions .
The first one deals with one of the most unresolved problems in astrophysics , i.e. , the existence of a blue loop after core helium ignition ; the so called ” to loop or not to loop ” problem .
We show that inward overshooting from the outer convective zone in the red giant phase is prerequisite for the development of the blue loop .
Our second question concerns pulsational instability of models in the core helium burning phase .
We present for the first time that models on the blue loop can have unstable modes driven by the \kappa mechanism operating in the Z - bump .
Contrary to post-main sequence models in the shell hydrogen burning phases , pulsational instability of the blue loop models depends mainly on effective temperature and metallicity is of secondary importance .
Finally , we try to interpret the oscillation spectrum of the blue supergiant HD 163899 , the only member of the SPBsg class , and to get some clue on the evolutionary status of the star .