* U.S. launches $75 billion mortgage modification plan

* Borrowers must show hardship to qualify for program

* Data show 1 in 5 homeowners owe more than house worth (Adds background; writes through)

By David Lawder and Lynn Adler

WASHINGTON/NEW YORK, March 4 (Reuters) - The Obama administration on Wednesday launched a $75 billion foreclosure relief plan, as new data showed one in five U.S. homeowners with mortgages owe more than their house is worth.

The mortgage plan, part of a $275 billion housing stimulus program announced last month, enables struggling homeowners to modify loans even if they are "under water."

Homeowners with mortgages on about 8.3 million properties were under water at the end of 2008 and the distress is likely to grow as home values drop, First American CoreLogic said.

The eligibility guidelines for the mortgage modification program unveiled by the U.S. Treasury aim to target relief to people facing imminent hardship. Their release opens the door for borrowers who are delinquent in their payments or at risk of falling behind to begin pressing for altered terms.

The program, which offers cash incentives to loan servicers to cut monthly payments, will only modify mortgages on single-unit homes up to $729,750, with higher limits for multiple-unit owner-occupied properties. It would only apply to loans originated before Jan. 1.