These reports present the results of the 2013 Community Summer Study of the APS Division of Particles and Fields (Snowmass 2013) on the future program of particle physics in the U.S. Chapter 6, on Accelerator Capabilities, discusses the future progress of accelerator technology, including issues for high-energy hadron and lepton colliders, high-intensity beams, electron-ion colliders, and necessary R&D for future accelerator technologies.