There really are no restrictions for traveling with the airlines during the first trimester of pregnancy. However, considering that a simple head cold can feel many times worse, or even the fact that it is often a challenge to put shoes back on that you may have removed during the course of a long flight, it is obvious that bodies are affected at some level when airborne. It is wise to make sure that your pregnancy is not threatened by air travel, and certainly if you are a frequent traveler, you may be advised to reduce the number of times you fly during pregnancy.
The second trimester is often seen as the safest time to travel during pregnancy, having moved through the tenuous first few months. Also, the second trimester is not full of risk for premature labor, unlike the third trimester which airlines can come to fear because of the possibility of premature labor, and the safety of the passengers. There are considerations like whether a seat belt can fit safely, economy class syndrome (or deep vein thrombosis - essentially blood clots that can form during long flights), and violent turbulence. Given such possible risks, it is again important for the pregnant passenger to verify that air travel will not complicate her pregnancy.
Most airlines do have some sort of policy, whether restrictive or not, when it comes to pregnancy and air travel. Surprisingly, not all of the airlines make this information readily available to its passengers that may be scouring their websites for their stand on transporting pregnant passengers. Because this information can be a hassle to find, this feature is a compilation of many of the airlines worldwide, and their respective policies when it comes to the acceptance of pregnant passengers, particularly during the third trimester. This feature includes airlines based in Europe and Africa, additional features include airlines based in the Americas, and Asia and Australia and New Zealand.
Bear in mind that the airlines will tend to take the word of the passenger as truth when it comes to how far along in the pregnancy she is, and airline representatives do not tend to be medical professionals. Thus the airline places the trust in the pregnant passenger to follow the airline's policy.
Next Pages - Airline Policies Regarding Pregnant Passengers

