It is recognised that high‐flow nasal therapy can prevent desaturation during airway management. Studies in spontaneously breathing patients show an almost linear relationship between flow rate and positive airway pressure in the nasopharynx. Positive airway pressure has been suggested as one of the possible mechanisms explaining how high‐flow nasal therapy works. However, data on pressures generated by high‐flow nasal therapy in apnoeic adults under general anaesthesia are absent. This randomised controlled crossover trial investigated airway pressures generated by different flow rates during high‐flow nasal therapy in anaesthetised and paralysed apnoeic patients, comparing pressures with closed and open mouths. Following induction of anaesthesia and neuromuscular blockade, a continuous jaw thrust was used to enable airway patency. Airway pressure was measured in the right main bronchus, the middle of the trachea and the pharynx, using a fibreoptically‐placed catheter connected to a pressure transducer. Each measurement was randomised with respect to closed or open mouth and different flow rates. Twenty patients undergoing elective surgery were included (mean (SD) age 38 (18) years, BMI 25.0 (3.3) kg.m^‐2, nine women, ASA physical status 1 (35%), 2 (55%), 3 (10%). While closed mouths and increasing flow rates demonstrated non‐linear increases in pressure, the pressure increase was negligible with an open mouth. Airway pressures remained below 10 cmH₂O even with closed mouths and flow rates up to 80 l.min⁻¹; they were not influenced by catheter position. This study shows an increase in airway pressures with closed mouths that depends on flow rate. The generated pressure is negligible with an open mouth. These data question positive airway pressure as an important mechanism for maintenance of oxygenation during apnoea.