Details of how atomic structure responds to strain are essential for building a deeper picture of mechanics in nanomaterials. Here, we provide the first experimental evidence of atomic displacements associated with shear strain in single-walled carbon nanotubes (SWNTs) by direct imaging using aberration-corrected transmission electron microscopy. The atomic structure of a zig-zag SWNT is resolved with unprecedented accuracy and the strain induced by bending is mapped in two dimensions. We show the existence of a dominant non-uniform shear strain that varies along the SWNT axis. The direction of shear is opposite to what would be expected from a simple force applied perpendicular to the axis to produce the bending. This highlights the complex atomistic strain behaviour of beam-bending mechanics in highly anisotropic SWNTs.