  The model of multiple Dirac eikonal scattering of incident proton by
target-nucleus nucleons is developed, in which new expressions for the elastic
$pA$-scattering amplitudes are obtained from the multiple scattering Watson
series with employing the eikonal approximation for the Dirac propagators of
the free proton motion between successive scattering acts on nucleons. Basing
on this model, calculations for the complete set of observables of the elastic
$p+^{40}$Ca and $p+^{208}$Pb at 800 MeV have been performed with using
proton-nucleon amplitudes determined from the phase analysis and the nucleon
densities obtained from describing the target-nucleus structure in the
relativistic mean-field approximation. A comparison has been made of the
results of these calculations with analogous calculations on the basis of the
Glauber multiple diffraction theory.
