Abstract. When the interplanetary magnetic field (IMF) encounters the Earth's magnetosphere, it is compressed and distorted. This distortion is known as draping, and plays an important role in the interaction between the IMF and the geomagnetic field. This paper considers a particular aspect of draping, namely how the orientation of the IMF in a plane perpendicular to the Sun-Earth line (the clock angle) is altered by draping in the magnetosheath close to the dayside magnetopause. The clock angle of the magnetosheath field is commonly estimated from the interplanetary magnetic field (IMF) measured by upstream monitoring spacecraft either by assuming that the draping process does not significantly alter the clock angle ("perfect draping") or that the change in clock angle is reasonably approximated by a gas dynamic model. In this paper, the magnetosheath clock angles measured during 36 crossings of the magnetopause by the Geotail and Interball-Tail spacecraft are compared to the upstream IMF clock angles measured by the Wind spacecraft. Overall, about 30% of data points exhibit perfect draping within ±10°, and 70% are within 30°. The differences between the IMF and magnetosheath clock angles are not, in general, well-ordered in any systematic fashion which could be accounted for by hydrodynamic draping. The draping behaviour is asymmetric with respect to the y-component of the IMF, and the form of the draping distribution function is dependent on solar wind pressure. While the average clock angle observed in the magnetosheath does reflect the orientation of the IMF to within ~30° or less, the assumption that the magnetosheath field direction at any particular region of the magnetopause at any instant is approximately similar to the IMF direction is not justified. This study shows that reconnection models which assume laminar draping are unlikely to accurately reflect the distribution of reconnection sites across the dayside magnetopause.