  The grid of evolutionary tracks of population II stars with initial masses
from $0.81M_\odot$ to $0.85M_\odot$ and chemical composition of the globular
cluster M 3 is computed. Selected models of horizontal branch stars were used
as initial conditions for solution of the equations of radiation hydrodynamics
and time--dependent convection describing radial stellar oscillations. The
boundaries of the instability strip on the Herztsprung--Russel diagram were
determined using nearly 100 hydrodynamic models of RR Lyr pulsating variables.
For each evolutionary track crossing the instability strip the pulsation period
was determined as a function of evolutionary time. The rate of period change of
most variables is shown to range within $-0.02\le\dot\Pi\le
0.05~\mathrm{day}/10^6\mathrm{yr}$. Theoretical estimate of the mean period
change rate obtained by the population synthesis method is
$\langle\dot\Pi\rangle=6.0\times 10^{-3}~\mathrm{day}/10^6\mathrm{yr}$ and
agrees well with observations of RR Lyr variables of the globular cluster M 3.
