The high temperature superconductivity in cuprates is realized by off-stoichiometric doping. In addition to contributing carriers to the CuO₂ planes, the dopants inherently introduce local disorder into the systems. Using the X-ray diffuse scattering technique, we studied the dopant-induced local structural distortions in two cuprate compounds: La₁.₉₂Sr₀.₀₈CuO₄ and YBa₂Cu₃O₆.₉₂. On La₁.₉₂Sr₀.₀₈CuO₄, strong anisotropic diffuse scattering pattern on top of the diffuse scattering due to thermal vibrations was observed. Our quantitative analysis shows that the observed anisotropic X-ray diffuse scattering intensities can be well described by the Huang Diffuse Scattering(HDS) theory with the single defect approximation, which indicates the Sr dopants are randomly distributed in the crystal. Based on the fitted parameters, the Sr-dopant induced elastic lattice distortion pattern was reconstructed. The big amplitude of the elastic lattice distortion near the Sr dopants suggests that Sr- dopant induced local structural modulation might be the origin of the electronic inhomogeneities observed with scanning tunneling microscopy experiments. The oxygen vacancies in YBa₂Cu₃O₆.₉₂ behave in a different way. Our X -ray diffuse scattering measurements reveal that majority of the oxygen vacancies tend to cluster together and are ordered to form a 4-unit-cell superstructure with $\ vec}q}_0$ = (1/4,0,0) along a* direction. The superlattice consists of large anisotropic displacements of Cu, Ba, and O atoms, respectively and appears to be consistent with the presence of an O-ordered "Ortho-IV'' phase. These ̀Òrtho-IV'' minority phase islands also induce long-range strains to the surrounding lattices, which manifest themselves as HDS observed in our experiments. Our quantitative analysis further revealed a b direction lattice modulation within the islands with the wavevector to be $\vec}q}_1=(0,0.21,0)$. The fact that $\ vec}q}_1$ is very close to the nesting vector connecting the nearly nested Fermi surface(FS) "ridges'' originated from the metallic Cu-O chains strongly indicates that the b direction modulation is induced by the FS effect