[en] Starting from the general eikonal approximation for the elastic scattering wave function of a nucleon on a system of A fixed scattering centers, whose spatial distribution is described by the squared ground state wave function of the target nucleus Φ_A(r₁...r_A) and excluding the NN potentials in favor of the NN scattering amplitude f(q) taken in eikonal approximation, the amplitude of the proton-nucleus, elastic, scattering is presented. For practical calculation a Gaussian parametrization was used. The developed approach was applied to description of the differential cross sections of the elastic scattering of protons with energy 600 and 1000 MeV on nuclei of ^2,3H, 3^,4He, which are considered in the model of the independent particles with nucleonic wave functions taken as the sums of Gaussian. The parameters of these functions are adjusted to reproduce the electromagnetic form-factors of the nuclei. In the limit of large A our expressions go over into the formulas of the optical model with the optical potential written in terms of the nuclear density and ω⁺(r). The numerical studies of the accuracy of the optical model expression have shown that it is reasonable even for s-shell nuclei. It appears that without additional fitting parameters our multiple center eikonal approximation allows to describe experimental angular distributions of the elastic scattering of protons on nuclei specified above much better than the standard diffraction theory. In particular, we were able to solve an old problem of deep diffraction minima in the differential cross sections, which could not be described in the traditional approach