Getting married without wedding rings?? Your thoughts?

My girlfriend and I are planning to elope this summer, marry in secret without the knowledge of family and friends. Neither of us have a lot of money, and wearing rings would probably give rise to suspicion from others. I know my girlfriend really wants a ring, and so do I. But it almost seems best to never get them. Should our vows be enough to symbolize our love and lifelong commitment to eachother? Is it weird that we don't have rings, even if we want them? I just don't want to short-change our day, and am afraid not having rings will make it less meaningful. Not only that, members of the opposite sex will think we're single. Your thoughts?