A new approach high-resolution electron microscopy combined with computer-imaging techniques is used to delineate the distorted atomic configurations that underlie the tweed structure in Y-Ba-Cu-O oxides. It appears that the quasi-periodic shear displacements along [110] anddirections are directly responsible for both the tweed contrast observed under the two-beam condition and the streaking in diffraction. The modulation is associated with the presence of off-stoichiometric oxygen occurring either when the trivalent elements substitute for Cu in the chain site or when oxygen is removed from YBa2Cu3O7.