Flexible and ultrathin wide-band metamaterial absorbers are suggested and demonstrated in the microwave-frequency range. By using resonators of different sizes and conductive fibers on metallic-pattern layer, the total thickness of metamaterial absorber is reduced to be only 1/349 with respect to the operating wavelength at 0.97 GHz. We present the absorption mechanism in terms of the impedance matching with the free space, the distributions of surface current and the three-dimensional distributions for power loss. In simulation, the absorption was over 97% at 0.97-6.12 GHz, and the corresponding experimental absorption band over 97% was 0.87-6.11 GHz. Furthermore, the dielectric substrate of metamaterial absorbers was replaced with flexible substrate in order to have the flexibility and the broadband absorption properties. The absorption band is expanded and the high-absorption performance maintains at the same time. The total thickness of metamaterial absorber comes to be only 1/5194 of the operating wavelength at 0.75 GHz. Our work is expected to contribute to the flexible microwave/electronic devices in the near future.