This study presents the transmission of electromagnetic waves through a partially covered narrow slot on a thick conducting screen when a plane wave is incident on the slot. The slot in the thick plate that creates a waveguide structure mainly causes resonance transmission (RT) above the cutoff; moreover, a weak RT (WRT) phenomenon also occurs. However, the WRT phenomenon has not been considered. In contrast, a partially covered slot in a thick plate creates a partially slotted waveguide (PSW). In the PSW structure, when the slot length is below the half-wavelength, WRT mainly occurs, even if the waveguide is above the cutoff, and RT does not occur. The amplitude of this WRT depends on the length of the slot and plate thickness. In addition, the transmission cross section (TCS) patterns with symmetry and asymmetry are presented with resonance states to consider the transmission mode in more detail.