The response of a nanographene sheet to external stresses was considered in terms of a mechanochemical reaction. The quantum chemical realization of the approach was based on the coordinate-of-reaction concept for the purpose of introducing a mechanochemical internal coordinate (MIC) that specifies a deformational mode. The related force of response is calculated as the energy gradient along the MIC, while the atomic configuration is optimized over all of the other coordinates under the MIC constant-pitch elongation. The approach is applied to the benzene molecule and (5,5) nanographene. A drastic anisotropy in the microscopic behavior of both objects under elongation along a MIC was observed when the MIC was oriented either along or normally to the C-C bond chain. Both the anisotropy and the high stiffness of the nanographene originate from the response of the benzenoid unit to stress.