Sawtooth structures are observed in tunneling probabilities with changing Planck's constant for a periodically perturbed rounded-rectangular potential with a sufficiently wide width for which instanton tunneling is substantially prohibited. The sawtooth structure is a manifestation of the essential nature of multiquanta absorption tunneling. Namely, the periodic perturbation creates an energy ladder of harmonic channels at E_{n}=E_{I}+nℏω, where E_{I} is an incident energy and ω is an angular frequency of the perturbation. The harmonic channel that absorbs the minimum amount of quanta of n=n[over ¯], such that V_{0}<E_{n[over ¯]}≤V_{0}+ℏω, makes a dominant contribution to the tunneling process, where V_{0} is the height of the static potential and V_{0}-E_{I}≫ℏω. At each steep slope part of the sawtooth structure, replacement of the dominant harmonic channel, i.e., E_{n[over ¯]}→E_{n[over ¯]+1}, occurs and the tunneling probability suddenly drops with increasing 1/ℏ. Due to the flatness of the potential top, resonance eigenstates exist just above the potential and the first resonance state appears as the peak of each edge of the sawtooth structure for the tunneling probability in the potential region. Sawtooth structures are also observed with changing the perturbation frequency. We introduce an effective formula to characterize the basic profile of those sawtooth structures.