Achieving stop band over broadband at low-frequency range has remained a great scientific challenge in spite of various efforts made using metamaterials or other technologies. In this work, we propose an idea that creates a stop band for broadband at low-frequency range. The dual mechanism of shear stiffening and rotation softening is initiated here to achieve a broad stop band at low-frequency range. Through analytical, numerical, and experimental studies, we reveal the underlying physical mechanism and confirm the effectiveness of this metamaterial on vibration shielding for flexural elastic wave covering 235 to 4520 Hz. This work opens an avenue for the development of elastic metamaterials with performance and functionalities that are highly desirable in many fields such as vibration shielding.