  Hydrodynamic models of short--period Cepheids were computed to determine the
pulsation period as a function of evolutionary time during the first and third
crossings of the instability strip. The equations of radiation hydrodynamics
and turbulent convection for radial stellar pulsations were solved with the
initial conditions obtained from the evolutionary models of population I stars
(X=0.7, Z=0.02) with masses from 5.2 to 6.5 Msol and the convective core
overshooting parameter 0.1 <= aov <= 0.3. In Cepheids with period of 4 d the
rate of pulsation period change during the first crossing of the instability
strip is over fifty times larger than that during the third crossing. Polaris
is shown to cross the instability strip for the first time and to be the
fundamental mode pulsator. The best agreement between the predicted and
observed rates of period change was obtained for the model with mass of 5.4
Msol and the overshooting parameter aov=0.25. The bolometric luminosity and
radius are L = 1.26e3 Lsol and R = 37.5 Rsol, respectively. In the HR diagram
Polaris is located at the red edge of the instability strip.
