  Evolutionary calculations of population II stars with chemical composition of
the globular cluster M3 were carried out under various assumptions about the
initial stellar mass ($0.809M_\odot\le M_\mathrm{ZAMS} \le 0.83M_\odot$) and
the mass loss rate parameter in the Reimers formula ($0.45\le\eta_\mathrm{R}\le
0.55$). In general, 30 evolutionary tracks of the horizontal branch stars were
computed. Selected models of evolutionary sequences were used as initial
conditions for solution of the equations of hydrodynamics that describe radial
stellar oscillations. Hydrodynamic models of RR Lyr type stars were computed
for the core helium burning stage as well as for the preceding pre--ZAHB stage.
Analytic relations for the effective temperature of the instability strip edges
as a function of stellar luminosity are obtained. Theoretical histograms of the
period distribution of RR Lyr type variables were produced for each
evolutionary sequence using Monte--Carlo simulations based on the consistent
stellar evolution and nonlinear stellar pulsation calculations. A satisfactory
agreement with observations (i.e. the greater number of RRab variables) was
found for the evolutionary sequence $M_\mathrm{ZAMS} = 0.811M_\odot$,
$\eta_\mathrm{R}=0.55$ with the number fraction of fundamental mode pulsators
$\approx 75\%$. At the same time the mean period of fundamental mode pulsators
($\langle\Pi\rangle_0=0.79$ day) is substantially greater compared to the
observational estimate of $\langle\Pi\rangle_\mathrm{ab}$.
