Five miles from the United States Supreme Court, a 40-foot-tall World War I memorial in the shape of a cross has stood for nearly a century. Now, it is at the center of a battle over the separation of church and state that may end up on the court’s docket.

The United States Court of Appeals for the Fourth Circuit declared this month that the Peace Cross, which sits on state-owned land in Maryland and has been maintained with public funds, was unconstitutional, a ruling that supporters of the monument warned could result in a “cleansing” of memorials on public grounds across the country.

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The Supreme Court ruled the displays unconstitutional, finding that they had no evident secular purpose. Michael W. McConnell, a constitutional law scholar at Stanford, calls such displays “triumphalism — a flavor of who is top dog.”

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The Peace Cross, also donated by a secular group, is almost twice as old as the monument in that case, and has been on public property for a comparable span. If the Supreme Court reviews this one, Mr. McConnell believes it will be squarely governed by Justice Breyer’s opinion.

“I think they thought they were putting this kind of case to rest with Van Orden,” said Mr. McConnell, who has also served as a judge in the Tenth Circuit Court of Appeals. “Somehow, the Fourth Circuit didn’t get the memo.”

“I think this is a pretty easy case, and I found the Fourth Circuit’s decision quite surprising. If the Supreme Court were to grant review, the likelihood is very high that it would be reversed.”