We experimentally and numerically demonstrate dual-mode resonances of electrically unconnected and connected U-shaped resonators array on flexible polyimide substrate in terahertz (THz) region. The unit cell consisting of two back-to-back U-shaped resonators (TUR) shows strong induction-capacitance resonance for TM mode and dipole resonance for TE mode. Then we clarify the transmission spectra characteristics of fourfold U-shaped resonators (FURs), which are composed of two twisted TUR at 90°. Distinct characteristic transmission responses are observed in varied coupled distances, specially, an “L-shaped” resonance is observed at connected FUR which does not exist in unconnected FUR. The polarization tunable property of TUR and polarization-independent characteristics of FUR are adequately clarified. Some applications such as polarization-tunable modulator (peak-to-peak value is about 0.4 for 90° polarization rotation) and polarization-independent dual-channel filter (full width with half maximum (FWHMs) nears to 85GHz) is proposed and verified experimentally, which may benefit to broaden novel ultrathin flexible THz devices.