As a last resort hire a professional rug cleaning company to steam the rug with a steamer or truck mount and dry it on an air table.
How to get ripples out of a rug.
Pull tacks with a carpet tack puller a small metal claw on a short thick shank or.
Smooth it as flat as you can and allow it to rest for a day or so.
Use the ice cube method for furniture dents.
Spritz the crushed area with enough water to saturate.
Always hold the hair dryer 6 to 9 inches away from the rug and use a sweeping motion.
If you don t have a large enough patch of sun flip the rug over and use a hair dryer to heat up the creases of the rug and release them.
The fibers will relax on their own.
What has worked for me is flipping the entire rug over and putting something heavy on the ripple.
The problem is you have to leave it like that for days but there seems to be no other way to work it out.
Again use a low heat setting when aiming your blow dryer toward the rug to avoid burning or melting the fibers.
A new rug may have waves or ripples in it when it s first unrolled.
Direct sunlight for several hours should help the rug release tension naturally and at the very least make it more supple for reverse rolling as noted in suggestion 1.
Pry the carpet gently up from the strips with a wood chisel or other pry tool on a wall parallel to the ripple.
It s possible to melt rug fibers so use a low or medium heat setting and keep the hair dryer moving back and forth at all times.
For these rugs if moisture is the problem the situation can sometimes be corrected by wetting the backing and tacking the rug out in a stretched position.
However the ripples may recur when moisture is again present.
Using a comb and a blow dryer gently brush out rug wrinkles.