This should, of course, be discussed with the pregnant woman's obstetrician. According to WebMD, air travel is generally ok during a normal, healthy pregnancy.

"I always tell my patients no travel after 32 weeks, because if she delivers, she won't have me there," says Elizabeth Nye, MD, an obstetrician at Rush Presbyterian St. Luke's Medical Center in Chicago. "She may have to deliver in a strange place with a doctor she has never met."

This page outlines some excellent suggestions for travelling during pregnancy:

http://www.webmd.com/baby/guide/traveling-while-pregnant

MayoClinic.com says:
"Generally, commercial air travel during pregnancy poses no special risks to a healthy pregnant woman or her baby. Still, if you're pregnant, it's best to check with your health care provider before you fly. Certain conditions in pregnancy — such as severe anemia, sickle cell disease, clotting disorders and placental insufficiency — can increase the risk of problems.

If you have flexibility in your travel plans, midpregnancy (14 to 28 weeks) may be the best time to fly. This is when you're likely to feel your best — and the risks of miscarriage and premature labor are the lowest. Your health care provider may restrict travel of any type after 36 weeks of pregnancy or if you're at risk of preterm delivery. "

http://www.mayoclinic.com/health/air-travel-during-pregnancy/AN00398

It is safe for a pregnant woman to travel by airplane as long as there are no complications involved in the whole course of pregnancy. You obstetrician will determine if is safe for you and your baby to travel by air. However, some airlines require you to present medical certificate to prove that you are in perfect health condition to travel by air. This is because many airline companies are afraid that you might deliver on board.

If you are going to take longer flights, make sure to exercise your leg and do some walking exercises inside the airplane. This increases the circulation on your feet thus minimizing the possibility of leg cramps. It is not advisable for a pregnant woman to stay seated the whole flight.

Flying is not contraindicated in uncomplicated pregnancy. However, if you experience any problems regarding your pregnancy, do not take the risks in traveling by air.

Yes pregnant women can fly on a plane as long as they are having a healthy pregnancy but it is suggested that women past their 36th week of pregnancy don't fly. And like any other business airports may have their own rules and restrictions. Some don't allow women to fly 30 before they are due, others it is seven, and some airport companies require a doctor's note that the pregnancy is normal and the baby healthy. You can read more about pregnancy and flying below. Hope this helps!