Observations of proton flux in the subsonic flow region of the magnetosheath show double peaks as a function of angle in the equatorial plane of the spacecraft. The peaks are separated by a wide angle, usually more than 90¿. Suggestions of double flux peaks are present in 95 percent of the data. They are interpreted as the effect of a persistent pressure anisotropy. The clearest cases were analyzed to determine the orientation of the flux peaks relative to the magnetic field and direction of model hydrodynamic flow. They are shown to be consistent with a greater pressure perpendicular to the field. Possible sources of pressure anisotropy in the magnetosheath are discussed.