  Excitation of radial oscillations in population I (X=0.7, Z=0.02) red
supergiants is investigated using the solution of the equations of radiation
hydrodynamics and turbulent convection. The core helium burning stars with
masses 8M_odot <= M <= 20M_odot end effective temperatures T_eff < 4000K are
shown to be unstable against radial pulsations in the fundamental mode. The
oscillation periods range between 45 and 1180 days. The pulsational instability
is due to the kappa-mechanism in the hydrogen and helium ionization zones.
Radial pulsations of stars with mass M < 15M_odot are strictly periodic with
the light amplitude Delta M_bol <= 0.5 mag. The pulsation amplitude increases
with increasing stellar mass and for M > 15M_odot the maximum expansion
velocity of outer layers is as high as one third of the escape velocity. The
mean radii of outer mass zones increase due to nonlinear oscillations by <= 30%
in comparison with the initial equilibrium. The approximate method (with
uncertainty of a factor of 1.5) to evaluate the mass of the pulsating red
supergiant with the known period of radial oscillations is proposed. The
approximation of the pulsation constant Q as a function of the mass-to-radius
ratio is given. Masses of seven galactic red supergiants are evaluated using
the period-mean density relation.
