ARLINGTON, Va. — The solemn ritual of a burial with military honors is repeated dozens of times a day, in foul weather or fair, at Arlington National Cemetery, honoring service members from privates to presidents. But in order to preserve the tradition of burial at the nation’s foremost military cemetery for future generations, the Army, which runs Arlington, says that it may have to deny it to nearly all veterans who are living today.

Arlington is running out of room. Already the final resting place for more that 420,000 veterans and their relatives, the cemetery has been adding about 7,000 more each year. At that rate, even if the last rinds of open ground around its edges are put to use, the cemetery will be completely full in about 25 years.

“We’re literally up against a wall,” said Barbara Lewandrowski, a spokeswoman for the cemetery, as she stood in the soggy grass where marble markers march up to the stone wall separating the grounds from a six-lane highway. Even that wall has been put to use, stacked three high with niches for cremated remains.

The Army wants to keep Arlington going for at least another 150 years, but with no room to grow — the grounds are hemmed in by highways and development — the only way to do so is to significantly tighten the rules for who can be buried there. That has prompted a difficult debate over what Arlington means to the nation and how to balance egalitarian ideals against the site’s physical limits.