The properties of suspended graphene are currently attracting enormous interest, but the small size of available samples and the difficulties in making them severely restrict the number of experimental techniques that can be used to study the optical, mechanical, electronic, thermal, and other characteristics of this one-atom-thick material. Here, we describe a new and highly reliable approach for making graphene membranes of a macroscopic size (currently up to 100 microm in diameter) and their characterization by transmission electron microscopy. In particular, we have found that long graphene beams supported by only one side do not scroll or fold, in striking contrast to the current perception of graphene as a supple thin fabric, but demonstrate sufficient stiffness to support extremely large loads, millions of times exceeding their own weight, in agreement with the presented theory. Our work opens many avenues for studying suspended graphene and using it in various micromechanical systems and electron microscopy.