  The deuteron-proton elastic scattering has been studied in the multiple
scattering expansion formalism. The essential attention has been given to such
relativistic problem as a deuteron wave function in a moving frame and
transformation of spin states due to Wigner rotation. Parameterization 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 MeV and
1200 MeV. The obtained results are compared with the experimental data.
