The observed cross sections of quasi-elastic scattering of 6 He, 7 Be, and 8 B nuclei by 12 C nuclei are described within the framework of the diffraction nuclear model and the model of nucleus-nucleus scattering in the high-energy approximation with a double folding potential, for intermediate energies of the incident particles. The calculations make use of realistic distributions of nucleon densities and take account of the Coulomb interaction and inelastic scattering with excitation of low-lying collective states of the target.