This article is from the Toyota Tundra FAQ, by Steve Yee with numerous contributions by others.
Well, I hate to tell you this, but this is normal.
Even though your tonneau cover frame is tight against the bed of the truck, and
the fabric is tight around the frame, two conditions occur that unfortunately
causes this flapping phenomenon: Fabric stretching and the physics of flying.
Let's face it, all fabric stretches to a certain degree. If they didn't
stretch, we'd all be running around bottomless after a really big Thanksgiving
dinner with two pieces of pie for dessert. The tonneau cover fabric will
stretch due to weather conditions, handling, and the physics involved in how
airplanes fly; all of this play big parts as to why your cover will bow and/or
Let's look at the physics of flight. The reason why airplanes fly is due to an
aerodynamic condition called lift. Lift is caused when there is a differential
in air pressure in one side of a surface versus the other side of a surface.
When your truck is moving, the air is moving faster over the tonneau cover
fabric than the air inside the bed of the truck. Therefore, your tonneau cover
will raise up and stretch to the limits of the fabric.
Your cover will flap around instead of bowing upward when the speed of your
truck is insufficient to provide enough consistent airflow to maintain lift.
If you don't like things flapping around, consider a Pace-Edwards type roll top
tonneau cover, or a SnugTop/A.R.E. type solid tonneau.