Stellar evolution calculations to the stage of the cooling white dwarf were done for population I stars with masses on the main sequence 1M ⊙ ≤ M 0 ≤ 1.5M ⊙ . The final helium flash LTP is shown to occur in post-AGB stars with initial masses 1.3M ⊙ ≤ M 0 ≤ 1.32M ⊙ for the overshooting parameter f = 0.016. In the case of more effective overshooting (f = 0.018) the final helium flash occurs at initial masses 1.28M ⊙ ≤ M 0 ≤ 1.3M ⊙ . Fivefold variations of the parameter responsible for the mass loss rate during the post-AGB stage do not affect occurrence of the final helium flash but lead to perceptible changes of the evolutionary time. Selected models of two evolutionary sequences with initial mass M 0 = 1.3M ⊙ computed with overshooting parameters f = 0.016 and f = 0.018 were used as initial conditions in solution of the equations of hydrodynamics describing radial oscillations of stars on the stage of the final helium flash at effective temperatures T eff < 10 4 K. The maximum pulsation period Π = 117 day determined for the evolutionary sequence M 0 = 1.3M ⊙ , f = 0.016 is in a good agreement with observational estimates of the period of FG Sge. The mass, the radius and the effective temperature of the star are M = 0.565M ⊙ , R = 126R ⊙ and T eff = 4445 K, respectively. At the same time the average period change rate of FG Sge from 1960 to 1990 is nearly three time larger than its theoretical estimate.