Anisotropic domains with 180° periodicity are known to be universally present on graphene as well as on other two-dimensional (2D) crystals. The physical origin of the domains and the mechanism of its anisotropy are, however, still unclear. Here, by employing in-plane elastic imaging by torsional resonance atomic force microscopy (TR-AFM), we demonstrate that the observed domains on graphene are of in-plane elastic (shear) anisotropy but not of friction anisotropy as commonly believed. Our results also support that the anisotropic domains originate from self-assembled environmental adsorbates on graphene surfaces. The more densely packed backbone of the highly ordered molecules within a domain defines the major axis of the shear anisotropy of the latter. This work suggests a quantitative understanding of the characteristics of anisotropic domains on 2D materials. It also demonstrates TR-AFM as a powerful tool to study the in-plane elastic anisotropy of materials, including organic molecular crystals.