Shinplaster is the common name for cheap paper money that was widely exchanged in the United States from 1837 to 1863, during the period known as the "Free Banking Period."

According to the Oxford English Dictionary, the name comes from the quality of the paper, which was so cheap that with a bit of starch it could be used to make paper mache-like plasters to go under socks and warm shins.

Sources

Rolnick, Arthur J. & Warren E. Weber, Free Banking, Wildcat Banking and Shinplasters," Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 6, No. 3, Fall 1982. http://minneapolisfed.org/research/qr/qr632.html