Abstract Cross sections for the elastic scattering of protons by He 4 have been measured for proton energies in the range 2⪅ E p ⪅ 11 MeV (lab system), using a tandem Van de Graaff accelerator and a differentially-pumped gas scattering chamber. Excitation functions, measured at centre-of mass angles 30.9°, 90.0°, 109.7° and 164.4° from E p = 4 to 11 MeV in 100–200 keV steps, showed no fine structure. Angular distributions were measured at 1 MeV intervals from E p =2 to 10 MeV with 1% counting statistics and scattering phase shifts were obtained from these data. An angular distribution was measured with less accuracy at E p = 11 MeV. The S-wave phase shift varies with energy as if scattering took place from a hard sphere of radius about 2.5 fm, whereas the P-wave phase shifts are well described by the effects of the ground and first excited states in Li 5, calculated using single-level dispersion theory. Little can be concluded from the behaviour of the D-wave phase shifts. The spin polarization of the scattered protons has been calculated from the phase shifts and is in satisfactory agreement with experimental results from other laboratories.