The elastic angular distributions for 9 Li + p and 11 Li + p at E lab /A = 60 and 62 MeV/ nucleon, respectively, have been analyzed within the framework of the eikonal model. It is assumed that 11 Li has the halo structure of a 9 Li core plus two weakly bound neutrons and is treated such that the nuclear potential has a sum of the core and halo neutron contributions. We have found that the break-up effect of halo neutrons is essential to understand the elastic cross sections of 11 Li + p system at E lab /A = 62 MeV/nucleon. The near-and the far-side decompositions of elastic cross sections have also been performed by following the Fuller's formalism. *