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This paper proposes a purely flexible lightweight membrane-type acoustic structure, wherein one kind of flexible lightweight rubber material takes the roles of mass and stiffness and another type of lightweight flexible EVA (ethylene–vinyl acetate copolymer) or plastic material functions as the localized stiffness for each unit. Because both the scatterers and base are constituted by the same material, this type of structure breaks the limitation that the metamaterials and phononic crystals need different materials with relatively large density and elasticity modulus ratios to play the roles of the scatterers and base respectively. Based on the band structures with different units, mass block shapes and size parameters, it is suggested that the shapes of the mass block can significantly affect the band structure. In addition, this type of structure could not only open a full band gap in the low-frequency range below 500 Hz, but also obtain an ultra-low-frequency bending wave band gap in the range below 100 Hz. Finally, we take into account the semi-infinite medium as a component, and calculate the sound transmission loss (STL) to evaluate the interaction between the structure and air. An experimental validation employing the cylindrical mass structure was developed to directly support the simulation results. Since the structures proposed in this study have achieved a purely flexible lightweight design, there exists an important promotion effect to realize the engineering applications of the acoustic metamaterials in practice. [ABSTRACT FROM AUTHOR]