We describe the magnetic string approach to integrating the dissipationless magnetohydrodynamic (MHD) equations for flow around planetary obstacles and apply it to some aspects of the flow in the magnetosheath of Venus. Our method has both analytical and numerical components and is particularly suited to study the structure of the magnetic barrier (depletion layer). We do not include ion pickup processes and thus discuss only the contribution to the structure of the Venus magnetosheath made by the flow of the shocked solar wind. We work with an interplanetary magnetic field which is directed orthogonal to the solar wind bulk velocity. Magnetic forces on the flow are strongly dependent on the Alfv¿n Mach number upstream of the bow shock, and one aim of this work is to study the dependence of field and flow quantities in the Venus magnetosheath on this parameter, thus allowing further future comparisons with data under a variety of interplanetary conditions. A second aim is to compare our MHD model results to a synopsis of observations made by the Pioneer Venus Orbiter. As one main conclusion, we show that this method leads, in principle, to a standoff bow shock position in good agreement with observations. We find, namely, that for a low but reasonable Alfv¿n Mach number, our MHD-modeled magnetosheath is only ~3.6% thinner in the Sun-Venus direction than that given by observations. Our method is complementary to three-dimensional, global MHD simulations of the solar wind--Venus interaction and offers versatility to modeling other aspects of the complicated interaction of the solar wind with Venus. ¿ 1999 American Geophysical Union