For rugs that wrinkle on top of wall to wall carpeting:
This usually happens when a rug is put on top of wall to wall carpeting. The wall to wall carpeting under the rug is too soft and the pressure from walking on it causes the rug to wrinkle up.There are special area rug pads (Super Move Not and Tiger Grip) that are made to go on the wall to wall carpeting. These pads may not be a permanent solution. You may periodically have to straighten the rug.
For new rugs that are wrinkled:
There is a possibility that there be could some wrinkled areas of your new rug.
Please note, this not a defect.
The rug has been bounced around in the shipping and handling.
Here are some of the best ways to smooth out a wrinkled rug.
You can spray a mist of some water on the top and back of the rug in the wrinkled areas. The moisture will relax the pile and the wrinkles will come out overnight.
You can reverse roll the rug in the opposite direction and leave it overnight.
You can use a hair drier on a low setting to soften the area.
Please be patient, eventually the wrinkles will come out in time with normal use.