  This paper provides a quantitative account of a recently introduced mechanism
of mechanical alignment of suprathermally rotating grains. These rapidly
rotating grains are essentially not susceptible to random torques arising from
gas-grain collisions, as the timescales for such torques to have significant
effect are orders of magnitude greater than the mean time between crossovers.
Such grains can be aligned by gaseous torques during the short periods of
crossovers and/or due to the difference in the rate at which atoms arrive at
grain surface. The latter is a result of the difference in orientation of a
grain in respect to the supersonic flow. This process, which we call
cross-section alignment, is the subject of our present paper. We derive
expressions for the measure of cross-section alignment for oblate grains and
study how this measure depends upon the angle between the interstellar magnetic
field and the gaseous flow and upon the grain shape.
