Within the framework of the Glauber diffraction theory, the differential cross sections of the elastic р 6 Не, p 8 Li, and p 9 Li scattering were calculated at intermediate energies from 70 to 1000 MeV/nucleon. The use of realistic three-body wave functions −n−n ( 6 He), −t−n ( 8 Li), and −t−2n ( 9 Li), obtained in the framework of modern nuclear models, and the expansion of the Glauber operator into a series of multiple scatterings in a form that is well adapted to the three-body nuclei configuration, allows the calculation of the matrix elements, by taking into account the rescattering from all structure components of the designated nuclei.