Share prices of Fannie Mae and Freddie Mac plunged Monday amid growing fears that the two largest providers of funding for U.S. home mortgages won't be able to avoid a government bailout.

In 4 p.m. trading on the New York Stock Exchange, Freddie shares were down 25% to $4.39. Fannie stock dropped 22% to $6.15. Both stocks are down more than 90% from a year ago.

Many...