A steady state two-dimensional model of the stratospheric ozone layer is presented. Chemical reactions involving oxygen, hydrogen, and nitrogen are considered along with the effect of a parameterized, two-dimensional transport, by mean motion and by eddies. The model is in reasonable agreement with observed ozone data. The reduction of ozone from emission of NOx from high flying aircraft is studied, assuming a fleet of 500 supersonic aircraft in transatlantic operation, flying at given altitudes. The effect is found to depend critically upon flight level. For mid-latitude, summer, the ozone column density is reduced by 0.3% for a flight level of 18 km. For flight levels of 23 and 28 km the reduction is 2 and 5%, respectively. Accordingly, the increase in u.v. radiation amounts to approximately 0.6, 4, and 10% for the same flight levels.