The weapons that we use in the sca are made out of rattan, nothing can be done to the rattan that changes its flexibilty.
"Swords" are usually shaved done on the sides and out of the back blades with a plane or spoke shave, once taped they can be no less than an inch and a quater in diameter and may be fitted with a thrusting tip, which is required to have and inch of pregressive give and may not double over.
thusting tips are usually contructed from close cell foam with a leather collar around the area that the rattan and the thrusting tip are joined to prevent doubling over.
Axes are considered a mass weapon* and thus cannot weigh more that 4 pounds, the head can be constructed out of several materials, the most common being close cell foam (like a camp mat) and must have progressive give over the whole head.
Maces often have a foam head with rattan splints attached to the outside, this is then taped over and is usaually attached to a handle(haft)that is relatively short and is also considered a mass weapon*
Two handed weapons such as the glaive, halberd and great sword are all mass weapons* and have many different methods of construction
It is a good idea to shape the handle of your weapon so that you can tell if you are hitting with the "blade" or the "flat" of your weapon.
*Mass weapons are those that have a weight limit of 4 pounds and have the added target areas of the hips and shoulders as kill zones.