Metamaterials (MMs) have become increasingly prominent in terahertz flexible devices. However, bending deformation often alters the structure of the unit, which affects the response performance and stability of MMs. Here, a metal-aperture metamaterial (MA-MM) utilizing the strong coupling effect induced by two resonance modes is innovatively proposed to address the mentioned limitations. Specifically, it is found that the coupling state between multiple resonance modes remains consistent at different bending angles. Under these circumstances, the generated Rabi splitting peak presents stable response performance even under low resonance intensity caused by excessive deformation. The experimental results demonstrate that despite the amplitude of two resonant peaks decreasing significantly by 87.6%, the Q-factor of the Rabi splitting only reduced by 14.8%. Furthermore, armed with the response mode of the Rabi splitting being unaffected by plasma excitation range, the designed MA-MMs are able to maintain constant Q-factors and frequencies on curved surfaces of varying sizes. These findings exhibit the characteristics of electromagnetic response for multi-mode resonance-coupled MA-MMs on different curved surfaces, presenting a novel design approach for terahertz flexible functional devices.