  The mode switching in Cepheids is studied using the methods of the nonlinear
theory of stellar pulsation, depending on the main sequence mass $M_0$ and the
abundance of elements heavier than helium $Z$. The grid of evolutionary and
hydrodynamic models of core--helium burning Cepheids is represented by 30
evolutionary sequences of stars with initial masses $5.7M_\odot\le M_0\le
7.2M_\odot$ and $Z=0.014$, 0.018, 0.022. For considered values of $Z$ the
periods of the fundamental mode and the first overtone at the oscillation mode
switching are shown to depend on the mean density of the stellar matter. The
upper limit of the period of the first overtone decreases witn increasing $Z$
from $\approx 6.9$ day for $Z=0.014$ to $\approx 4.1$ day for $Z=0.022$. The
theoretical period--radius relation is independent of $Z$ and agrees well
(within 2.5\%) with recent measurements of Cepheid radii based on the
Baade--Wesselink method. The fundamental parameters of the short--period
Cepheid CG Cas were derived with application of observational estimates of the
period and the rate of period change. This star is shown to be the
first--overtone pulsator.
