Résumé : We employ a microscopic continuum-discretized coupled-channels reaction framework (MCDCC) to study the elastic angular distribution of the 7Li=α+t nucleus colliding with C12 and Si28 targets at ELab=350 MeV. In this framework, the Li7 projectile is described in a microscopic cluster model and impinges on noncomposite targets. The diagonal and coupling potentials are constructed from nucleon-target interactions and Li7 microscopic wave functions. We obtain a fair description of the experimental data, in the whole angular range studied, when continuum channels are included. The inelastic and breakup angular distributions on the lightest target are also investigated. In addition, we compute 7Li+12C MCDCC elastic cross sections at energies much higher than the Coulomb barrier and we use them as reference calculations to test the validity of multichannel eikonal cross sections. © 2014 American Physical Society.