The advisability of flying whilst pregnant is a frequently asked question.
The commercial aircraft environment is not generally considered hazardous to the normal pregnancy. At a normal cabin altitude the maternal haemoglobin remains 90% saturated and because of the favourable properties of foetal haemoglobin (HbF) including increased oxygen carrying potential plus increased foetal hematocrit and the Bohr effect, foetal PaO2 changes very little.
The key focus in assessment of fitness to fly is the health and wellbeing of the mother and the baby. Delivery in flight, or diversion in flight to a location, which may not have high quality obstetric services, is undesirable. For this reason, most airlines do not allow travel after 36 weeks for a single pregnancy and after 32 weeks for multiple pregnancies.
Most airlines require a certificate after 28 weeks, confirming that the pregnancy is progressing normally, that there are no complications and the expected date of delivery. In specific individual circumstances, an airline may allow some discretion.