Sigh… so many answers are getting things backwards, or just plain wrong.
Commercial airplanes don’t fly at 35–38k feet because of their coffin corner, commercial airplanes’ coffin corner is what it is because airlines want to fly at 35–38k. Airlines don’t fly at 35–38k feet because of the maximum pressure differential they can withstand; the maximum pressure differential planes can withstand is what it so airlines can fly at 35–38k feet.
Commercial airplanes are designed to fly at 35–38k feet because airlines want to fly at that altitude. Simple as that. But why do airlines want to fly at that altitude? Two reasons:
- You are above the weather, which results in flight being easier, cheaper, more comfortable, etc
- Above the weather, 35–38k feet is the most efficient altitude to fly.
#2 requires more explanation. The higher you go, the thinner the air, resulting in less drag, meaning higher altitudes are more efficient. But the higher you go, the larger the pressure differential between inside and outside the plane, meaning the plane has to be built stronger, meaning lower altitudes are more efficient. Likewise, the higher you want to fly, the stronger your engines need to be to get to that altitude, again making lower altitudes more efficient.
So, if for some aspects of a plane’s design, higher altitudes are better, but for others lower altitudes are better, what makes 35–38k feet the sweet spot? As it turns out, 35–38k feet is the sweet spot not because of drag, or air density, or pressure differential, or any other reason I’ve seen mentioned in other answers. 35–38k feet is the sweet spot because of temperature.
In order for an airplane to operate as efficiently as possible, in addition to having the most efficient design, you also need the engines to operate as efficiently as possible. And aircraft engines operate most efficiently when the temperature difference at their inlet and inside the engine is maximized. Because of this, the colder the outside temperature, the more efficiently the engines operate.
Well, the higher you go the colder it gets, so airplanes should just continue increasing their altitude forever, right? Wrong. The higher you go the colder you get until you reach ~35k feet, at which point the temperature stops decreasing and remains constant. Then, at ~50–60k feet, the temperature actually starts warming again!
IMAGE SOURCE: www.weather.gov
So basically, at ~35–50k feet, airplane engines stop increasing their efficiency. And at this altitude, the increased efficiency given by lower altitudes outweighs the increased efficiency given by higher ones. Hence 35–38k feet is the most efficient altitude for aircraft to fly at. Because of this, for a commercial airliner, every cruise level flight design aspect (coffin corner, pressure differential, lift, drag, max thrust, etc) is designed around this altitude, and this is the altitude those planes fly at.
SOURCE: I studied Aerospace engineering and then worked for a year at Boeing in their commercial airplane division
EDIT: stop mentioning FAA regulations. Those regulations are what they are in part because of what I wrote above. If flying at 50k feet cost half as much as flying at 35k, airlines would fly at 50k, and honestly, if this were the case, FAA regulations most likely wouldn’t be what they currently are. FAA regulations kick in above the height where airplane efficiency starts maximizing; this is not a coincidence and if airplane efficiency started maximizing higher, airlines and the FAA would work together to ensure regulations allowed airlines to fly there.