20-25% of persons suffer from this, and it can have a serious impact on the life choices of a sufferer, and even their family. It is a learned response to aircraft and it can be 'unlearned' with the right help. The Wikipedia entry on fear of flying calls it Pteromerhanophobia, ... a fear of being on an airplane (aeroplane), or other flying vehicle.. It is also sometimes referred to as aerophobia, aviatophobia, or aviophobia. Fear of air travel is a recognised “phobia” but it is rarely just a fear of travelling on a plane. The flying phobia is usually based in a more basic fear such as fear of enclosed spaces (claustrophobia) or fear of not being able to escape from a situation (agoraphobia) or even a fear of heights.
The first step in beating the fear of flying is evaluation of the underlying psychology; finding the triggers and separating them from the fear of flight. Often these are of such low level that they do not cause discomfort in everyday life and can be difficult to unravel. If there is an identified general anxiety disorder there is a great deal that a psychologist can offer. After a clear evaluation is concluded, psycho-education is beneficial. Fear is usually fear of the unknown rather than the known or as Roosevelt said “fear of fear”. Education includes knowledge of the checking processes, the causes of turbulence, and the science of flight. The knowledge that the process of flight has similarities to the operating theatre is usually reassuring. Medication has a role but a recent Harvard study indicated that relieving the anxiety of flight with medication increased the anxiety of any future flight and increased the need (and dose) for medication. Australia has a great website and service: fearless flyers. Fearless Flyers Inc. is a Non-Profit, volunteer organisation run by women pilots since 1979 in association with Qantas Airways Ltd and Airservices Australia. They report that it is the second oldest course in the world with in in excess of 1,500 graduates Books are available with practical tips for those who don't suffer too severely e.g. here and here and here There is even an app to help. Help is available - you don't have to suffer in silence.