We investigate the MHD structure of the Jovian magnetosheath along the Sun-Jupiter line and, particularly, the region where the interplanetary magnetic field (IMF) exerts a large influence on the magnetosheath flow (the ''magnetic barrier''). We do this by integrating numerically the dissipationless MHD equations in their ''magnetic string'' formulation. The lack of axisymmetry of the magnetospheric obstacle introduces corresponding asymmetries in the Jovian magnetosheath. The dominant effect on the flow is produced by the IMF component orthogonal to Jupiter's rotational equator. The thicknesses of the magnetosheath and magnetic barrier depend sensitively on the orientation of the IMF, decreasing monotonically as the inclination of the IMF to the rotational equator decreases. The magnetic barrier practically disappears when the IMF vector lies in the equator. For an arbitrary orientation of the IMF the magnetosheath magnetic field along the stagnation streamline is not only compressed as the magnetopause is approached but also rotates smoothly toward the direction of the Jovian rotation axis. This effect is absent in the case of flow around axisymmetric obstacles, such as the terrestrial magnetosphere. ¿ American Geophysical Union 1996