The deuteron-proton elastic scattering is studied in the multiple scattering expansion formalism. The contributions of the one-nucleon-exchange, single- and double scattering are taken into account. The Love and Franey parameterization of the nucleon-nucleon $t$-matrix is used, that gives an opportunity to include the off-energy-shell effects into calculations. Differential cross sections are considered at four energies, $T_d=390, 500, 880, 1200$ MeV. The obtained results are compared with the experimental data.