A suspension for a washing machine and a washing machine with the suspension is disclosed. The suspension includes a support shaft; a first elastic member that surrounds a portion of the support shaft and provides a first elastic force to the support shaft in a longitudinal direction of the support shaft; a second elastic member between the support shaft and the first elastic member, and configured to provide a second elastic force different from the first elastic force to a support shaft in the same direction as the first elastic member; a guide stopper at one end of the support shaft, configured to restrict movement of the first elastic member and the second elastic member in one direction; and a housing on the support shaft that surrounds the first and second elastic members, configured to restrict movement of the first and second elastic members in another direction.