Rolled oats, whole wheat, brown rice and buckwheat groats all contain large amounts of fiber. When grain is milled in the modern way, however, most of the fiber is lost. Both the bran, the outer layer of the kernel, and the endosperm, the germ or central portion, have been removed from the white flour. The best vegetable sources of fiber are the leafy vegetables -asparagus, celery, broccoli, brussels sprouts, cabbage, cauliflower and lettuce. Root vegetables like carrots, radishes and turnips also have high amounts of fiber, as do yams, beans, peas and corn.
White potatoes contain fiber, although most of it is in their skins.
Nuts are a particularly good source of fiber. Not measurably, even though cooking changes the consistency. But there is some evidence that fiber can be destroyed by pounding, grinding or mashing. It's possible, but unlikely. Certain intestinal problems have been shown to be more common in fiber-eating populations.