The transfer of energy from the moving air in the shear wind above the sea surface to a bird is considered as an energy source for dynamic soaring, with the goal to determine the minimum shear wind strength required for the dynamic soaring of albatrosses. Focus is on energy-neutral trajectories, implying that the energy gain from the moving air is just sufficient to compensate for the energy loss due to drag for a dynamic soaring cycle. A mathematical optimization method is used for computing minimum shear wind energy-neutral trajectories, using a realistic flight mechanics model for the soaring of albatrosses. Thus, the minimum shear wind strength required for dynamic soaring is determined. The minimum shear wind strength is of a magnitude that often exists or is exceeded in areas in which albatrosses are found. This result holds for two control cases dealt with, one of which shows a freely selectable and the other a constant lift coefficient characteristic. The mechanism of energy transfer from the shear flow to the bird is considered, and it is shown that there is a significant energy gain in the upper curve and a loss in the lower curve. As a result, the upper curve can be qualified as the characteristic flight phase of dynamic soaring to achieve an energy gain.