Instability of population I (X=0.7, Y=0.02) massive stars against radial oscillations during the post-main sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range from 65M_\odot to 90M_\odot. In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is Teff > 6700K for Mzams=65M_\odot and Teff > 7200K for mzams=90M_\odot. Pulsational instability is due to the \kappa-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed 200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is Teff > 7300K for Mzams=65M_\odot and Teff > 7600K for Mzams=90M_\odot. Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (Teff > 7700K for Mzams=65M_\odot and Teff > 8200K for Mzams=90M_\odot). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed 130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.