The United States Tennis Association will spend an estimated $500 million through the coming decade to build a new Louis Armstrong Stadium, a new grandstand on unused land at the Billie Jean King National Tennis Center, and a double-deck viewing area for fans to watch players practice during the United States Open.

But the plans do not include a roof over Arthur Ashe Stadium or the new Armstrong facility.

Rain delays have caused the United States Open men’s final to be played on a Monday for the past four years, increasing calls for the Open to join the other three Grand Slam events in adding a roof on at least one showcase court. Melbourne Park, site of the Australian Open, has retractable roofs on two courts and plans for a third; Centre Court at Wimbledon gained its retractable roof in 2009; and a new center court with a retractable roof is expected to open at Roland Garros in 2017.

U.S.T.A. officials said that Arthur Ashe Stadium, which was built on a swamp-like ash dump, could not physically absorb the weight of a roof that would cover its expanse.

“It’s five times larger than the span that covers Wimbledon,” said Gordon Smith, the U.S.T.A.’s chief operating officer.