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Abstract We present a pioneering model of the interaction between the solar wind and the surrounding interstellar medium that includes the possibility of different pressures in directions parallel and perpendicular to the magnetic field. The outer heliosheath region is characterized by a low rate of turbulent scattering that would permit development of pressure anisotropy. The effect is best seen on the interstellar side of the heliopause, where a narrow region develops with an excessive perpendicular pressure resembling a plasma depletion layer typical of planetary magnetospheres. The magnitude of this effect for typical heliospheric conditions is relatively small owing to proton–proton collisions. We show, however, that if the circumstellar medium is warm and tenuous, a much broader anisotropic boundary layer can exist, with a dominant perpendicular pressure in the southern hemisphere and a dominant parallel pressure in the north.