The wavelike oscillations of the vertical scale height of the local population of classical Cepheids located at Galactocentric distances R0 – 1 kpc < Rg < R0 + 1 kpc is analyzed using Cepheid ages computed in terms of evolutionary models of Pols et al. (1998) with and without the allowance for convective overshooting. The resulting periods of vertical oscillations of stars about the galactic plane are found to be PZ = 74 ± 2 Myr and PZ = 104 ± 2 Myr for standard models and models with overshooting, respectively. If interpreted as a manifestation of vertical virial oscillations, the pattern found implies local mass density values of ρstd = 0.118 ± 0.007 M⊙ pc−3 and ρovs = 0.060 ± 0.004 M⊙ pc−3, respectively. The latter value is totally incompatible with recent estimates based on Hipparcos data and the former value, combined with recent estimates of the local density of visible matter, sets an upper limit of 0.023 M⊙ pc−3 for the local density of dark matter.