Evolutionary calculations of population I stars with initial masses M 0 = 1M ⊙ , 1.5M ⊙ and 2M ⊙ were carried out up to the stage of the proto-planetary nebula. Selected models of post-AGB evolutionary sequences with effective temperatures 3.6 × 10 3 K T eff 2 × 10 4 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 Π ≈ 300 day to several days. Period fluctuations are due to nonlinear effects and are most prominent at effective temperatures T eff < 5000 K. The amplitude of bolometric light variations is ∆M bol ≈ 1 at T eff 6000 K and rapidly decreases with increasing T 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. 1 introduction The red giant evolutionary stage of stars with solar composition and the zero-age main sequence mass M 0 9M ⊙ is completed due to the strong stellar wind and the loss of the major fraction of the hydrogen envelope. The star leaves the asymptotic giant branch (AGB) and crosses the Hertzsprung-Russel diagram (HRD) at nearly constant luminosity towards the region of planetary nebula cores with effective temperatures T eff ∼ 10 5 K. An idea that the planetary nebulae originate from red giants was suggested by Shklovsky (1956) and was later confirmed by evolutionary computations (PaczyńskiFormation of the opaque gas-dust envelope surrounding the star on the tip of the AGB substantially restricts abilities of optical observations, so that the evolutionary transition to the post-AGB stage still remains unclear. The strong stellar wind on the tip of the AGB seems to be due to nonlinear stellar pulsations that lead to dynamical instability of the outer stellar layers (Tuchman et al., 1978). Therefore, large infrared (IR) excesses detected in post-AGB stars (Volk, Kwok, 1989; Hrivnak et al., 1989; 1994; Ikonnikova et al., 2018) indicate existence of circumstellar dust grains condensed during the preceding evolutionary stage with high mass loss rates. The photometric variability due to stellar pulsations is a typical property of post-AGB stars. The period of light variations ranges from several dozen days (Arkhipova et al., 2010; Hrivnak et al.2015; 2018) to Π ≈ 200 day (Arkhipova et al. Ikonnikova et al., 2018). Moreover, the pulsating variable AI CMi with period Π ≈ 310 day seems to be the early post-AGB star (Arkhipova et al., 2017). A common feature of post-AGB stars is a lack of strict repetition in light variations, so that observational estimates of the period are often highly uncertain.The post-AGB stars are on the late...