The mechanical properties of graphene are as impressive as its electronic properties. Some idea of its rigidity can be judged by saying that scaling the thickness to a sheet of paper, the paper could form a horizontal cantilever 100 m long. A cantilever of graphene should act as a very high Q mechanical oscillator and the frequency shift when molecules are attached to it, on sensitised sites, could make it into a very sensitive detector of specific molecules. The combination of the light atomic mass and the very stiff lattice structure makes the velocity of elastic waves in graphene very large, and so the phonon Debye temperature is extremely high and the number of thermal phonons relatively low. The thermal conductivity is very high too, comparable with diamond. The phonons in graphene must be understood because they scatter electrons and limit the electron mobility. If the graphene is on a substrate, then the phonons in the substrate also scatter the electrons. The mechanical, thermal and phonon properties of graphene, on different substrates, including no substrate, will be investigated experimentally and theoretically with a view to devices.