Excitation of atoms from the ground quantum level to a metastable state by traveling monochromatic radiation in a thin gas cell, the internal thickness of which is much smaller than its radius, is studied theoretically. Sub-Doppler resonances are detected and analyzed that arise in the population of a metastable atomic level due to light-induced Rabi oscillations on a given optical transition and specific features of transit-time relaxation of atoms in a considered cell with a rarified gas upon scanning the radiation frequency. Such nontrivial resonances can be recorded in fluorescence of atoms with the help of an additional probe light beam. A method is proposed for a direct measurement of the Rabi frequency from spectral intervals between detected sub-Doppler resonances. The results obtained can be applied in atomic spectroscopy for the precision determination of components of dipole moment matrix elements, as well as for the Einstein coefficients and oscillator strengths related to these components, for quantum transitions between the ground and metastable levels of atoms.