We have measured the differential cross-section and the analyzing power (polarization) for $p$-$^{4}\mathrm{He}$ elastic scattering at incident kinetic energies of 0.56, 0.80, 1.03, 1.24, and 1.73 GeV. The experiment used a polarized proton beam incident on a liquid helium target and a single arm magnetic spectrometer to detect elastic scattering. Both the differential cross sections and the analyzing power show structure near $\ensuremath{-}t=0.25$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ which decreases in magnitude with increasing energy. Both multiple scattering and optical model interpretations of the data are discussed.NUCLEAR REACTIONS elastic scattering, $p$-$^{4}\mathrm{He}$; GeV energies; measured differential cross section; measured polarization; comparison with theory.