The Princess Bride star has an outstanding debt of $26,207.82 (£16,192.66), according to TMZ.
Elwes's debt covers the years 2010 and 2011 and is owed to California's Franchise Tax Board.
The actor has not issued any comment on the alleged financial trouble.
He is known for a string of high-profile roles in the 1980s and early 1990s, including Hot Shots, Robin Hood: Men in Tights and the Alicia Silverstone breakthrough The Crush.
Elwes has most recently appeared in the Saw series and New Year's Eve.
Watch the original trailer for The Princess Bride below: