We describe studies of the elastic properties and frictional characteristics of graphene samples of varying thickness using an atomic force microscope. For tensile testing, graphene is suspended over micron-sized circular holes and indented by atomic force microscope (AFM) tips. Fitting of the force-displacement curves yields the prestress and elastic stiffness, while comparison of the breaking force to simulation gives the ultimate strength, which is the highest measured for any material. Experiments on samples with 1–3 atomic layers yield similar values for the intrinsic stiffness and strength of a single sheet, but also reveal differences in mechanical behavior with thickness. The frictional force between an AFM tip and graphene decreases with thickness for samples from 1 to 4 layers, and does not depend on the presence of a substrate. High-resolution friction force imaging in stick-slip mode shows the same trend, and allows direct imaging of the crystal lattice.