Briars in general are not pleasant things to deal with because the vines have sharp thorns. These plants are not typically satisfactory in lawns and gardens. There are several ways to get rid of them, but only one method proves to be permanent.
Dig up all the briars and place them into the wheelbarrow. When you're done, the ground should look like freshly tilled ground.
Put the plants into a fire pit and douse them with gasoline or lighter fluid. Light the fire immediately, especially if using gasoline. Allowing the gasoline to sit for any amount of time encourages the movement of the fumes, which also ignite, so in order to prevent an explosion of any magnitude, light the fire immediately.
Excerpted from eHow.com, How to Get Rid of Briar Patches