  Evolutionary calculations of population I stars with initial masses
$M_0=1M_\odot$, $1.5M_\odot$ and $2M_\odot$ were carried out up to the stage of
the proto--planetary nebula. Selected models of post--AGB evolutionary
sequences with effective temperatures $3.6\times 10^3\,\mathrm{K}\lesssim
T_\mathrm{eff}\lesssim 2\times 10^4\,\mathrm{K}$ were used as initial
conditions in calculations of self--escited stellar oscillations. For the first
time the sequences of hydrodynamic models of radially pulsating post--AGB stars
were computed using the self--consistent solution of the equations of radiation
hydrodynamics and time--dependent convection. Within this range of effective
temperatures the post--AGB stars are the fundamental mode pulsators with period
decreasing as the star evolves from $\Pi\approx 300$ day to several days.
Period fluctuations are due to nonlinear effects and are most prominent at
effective temperatures $T_\mathrm{eff} < 5000$K. The amplitude of bolometric
light variations is $\Delta M_\mathrm{bol}\approx 1$ at $T_\mathrm{eff}
\lesssim 6000$K and rapidly decreases with increasing $T_\mathrm{eff}$. The
theoretical dependence of the pulsation period as a function of effective
temperature obtained in the study can be used as a criterion for the
evolutionary status of pulsating variables suspected to be post--AGB stars.
