The present application generally relates to orthopedic stabilization systems, and in particular, to systems including clamps. The clamps can be used in addition to or to replace hooks that grasp onto bone members, such as the lamina. One example of such a clamp is an in-line clamp that includes a central opening for receiving a rod member, a first opening for receiving a set screw and a second opening for receiving an elastic member therethrough. Another example of such a clamp is an off-set clamp that includes an upper plate, a bottom plate, and an opening for receiving a rod therein. The upper plate can be separated from the bottom plate to make space for an elastic member that can be secured within the plates. Tulip clamps that utilize one or more elastic members are also provided.