You see, getting rid of a Woodchuck takes a ruthlessness and resolve that does not come easily to human beings. The animals' burrows have two holes for entering and exiting. The trick is to find the "escape hole," plug that up, throw smoke bomb in the main entrance, and then plug that up. One person I know who had extinguished their pest problem in this way, said it had been a hard thing to do, but noted that if they had not taken such drastic measures they would have lost their entire garden.
Did you know that a Woodchuck is the same thing as a Ground Hog? According to Wikipedia, "the etymology of the name woodchuck is unrelated to wood or chucking. It stems from an Algonquian name for the animal (possibly Narragansett), wuchak"

