[en] The deuteron-proton elastic scattering has been studied in the multiple-scattering expansion formalism. Primary attention has been given to such relativistic problems as a deuteron wave function in a moving frame and transformation of spin states due to Wigner rotation. Parametrization of the nucleon-nucleon t matrix has been used to take the off-energy-shell effects into account. The vector, A_y, and tensor, A_yy, analyzing powers of the deuteron have been calculated at two deuteron kinetic energies: 395 and 1200 MeV. The obtained results are compared with the experimental data.