The position of the Giotto spacecraft relative to comet Grigg-Skjellerup is found from the draping geometry based on the vector magnetic field data. It is shown that Giotto passed the cometary nucleus on the nightside. The behavior of the magnetic field vectors exhibits two different types in the pileup region. In the outer pileup region, the magnetic field vectors converge toward the nightside in accordance with the flank draping observed earlier near comet Halley. The existence of the flank draping is a consequence of a three-dimensional plasma flow around the comet: a slippage of magnetic field lines on the flanks of the obstacle results in this effect. Because of this slippage, only a fraction of the incoming magnetic flux takes part in the formation of the magnetic barrier and the magnetic tail, whereas most of the magnetic flux bypasses a comet from both sides. In the inner pileup region, the magnetic field vectors diverge toward the nightside. This effect is attributed to the plasma flow into the cavity behind the obstacle. ¿ American Geophysical Union 1996