We present here the fabrication of large suspended sheets of graphene for mechanical resonators. The diameter of the circular resonators varies from 1.2 μm to 26.5 μm resulting in diameter-to-thickness aspect ratios as large as 74000. The membranes were fabricated in arrays with yields of up to more than 90%. Assuming low to moderate tensile stress, <1 GPa, the mechanical resonance frequency of these structures potentially spans the range from ~1 MHz to ~1 GHz. The successfully fabrication of graphene membranes will allow us to first study their mechanics (resonance frequency and damping) and later explore their use for various sensing applications, including mass sensing.