Résumé : The elastic scattering of K+ mesons on protons is studied at 3.5 and 5 GeV/c. The total elastic cross-sections are found to be (4.36±0.36) mb and (3.82±0.41) mb respectively. The differential elastic cross-sections, which exhibit characteristic diffraction peaks, are fitted by dσ/d t=(dσ/d t)0 e αt, giving α=(3.85±0.12) and (4.70±0.21) (GeV/c)-2 for the two momenta respectively, with