Atomic vibrations control all thermally activated processes in materials, including diffusion, heat transport, phase transformations and surface chemistry. Recent developments in scanning transmission electron microscopy (STEM) have enabled nanoscale probing of vibrational modes using electron energy-loss spectroscopy (EELS)1,2. Although atomically resolved analysis is routine in STEM, vibrational spectroscopy employing oscillating dipoles yields signals originating from regions tens of nanometres in size, because the scattering angles are only a few microradians3. Recently, it has been shown that energy-filtered images recorded at high scattering angles display atomic resolution4. Here we show, using conventional on-axis EELS, that non-dipole, impact scattering vibrational signals are present, and exhibit atomic resolution. This on-axis signal shows variations in the spectral peak shape and intensity as the electron probe is scanned across an individual atomic column in a Si sample. Although atomic spatial resolution in coherent elastic scattering will complicate the quantitative interpretation of spectra from crystals, the change in peak shape provides compelling evidence that the vibrational EELS excitation process is highly localized. High spatial resolution is also demonstrated in SiO2, an amorphous polar material. Our approach represents an important technical advance that will provide new insights into the local thermal, elastic and kinetic properties of materials.