Two interesting things about elephants, and one interesting thing about the president:

Elephants walk flat-footed, but faster than you might think, and covered the 8.5 miles between the Eckington train yards and the White House yesterday morning in just an hour.

Elephants understand language. Upon being asked, trained elephants will sit, do a left face or stand on their hind legs (that command is "Trunk !"). They seem eager to please in a large way.

When the elephants appeared outside his house yesterday morning, Ronald Reagan pressed his nose near the glass of an upstairs window and waved vigorously for five minutes or more, often with both hands over his head. His side must be sore, but his movement is clearly not constrained.

The occasion was a 21-elephant salute put on by Ringling Bros. and Barnum & Bailey Circus, and the elephants came complete with jugglers, costumed ladies and a banner that read "Welcome Home Mr. President." The highlight of the visitation was a classic "long mount" in the middle of Pennsylvania Avenue, in which each elephant placed its forelegs on the back of the one in front of it.

Then the elephants walked on to the Armory, where the circus opened last night. The White House had no formal comment to make, but confirmed that the president had waved.

On the way from the train yards, a three-ton elephant was ridden by a 50-pound little girl named Silvy Nordquist, who is in the third grade at Holton Arms School. She won the elephant ride in a raffle. Nordquist commented that the skin of an elephant is "rough and warm." She had no trouble getting to sleep the night before, she said.

Michael "Tuba" Heatherton preceded the elephants down Pennsylvania Avenue.He was strapped into stilts that made him 10 feet tall and afforded a fine view of President Reagan in the window. Heatherton, as he walked along, called down gently to ask that other pedestrians clear a path for him. "If you're on stilts and you fall, you get hurt," he confirmed. "But at least you can keep from falling on someone else."

Elephants stopped traffic for about 15 minutes, but Washington, D.C., was not born yesterday and nobody seemed notably surprised. Elephants were no harder to explain than the White House lawn sprinkler system, which was going full blast even though it had rained heavily in the night, and Lafayette Park, at least, was soggy as an overcooked cabbage.

R. Lansberry, of Post Office Box 1153 in Pittsburgh, watched from the sidewalk. He was wearing a sandwich board which advertised his complaint. Lansberry says he is a consumer advocate who receives funds in the mail, but that someone or something in Washington is preventing him from getting the mail that is rightfully his. The elephants did not bother him. "I'm normal," he explained.

Allen Bloom, wearing a cigar and a nicely cut sports jacket, was pleased with the elephant walk. He is vice president for marketing and sales for Ringling Bros. "Yes," he said in answer to the question, "Are elephants really smart?"

As animals will, the 21 elephants left Pennsylvania Avenue a large amount of material to remember them by. Specifically, the owner of Red Ford Landau D.C. 556-738, whose automobile formed the rear end of an elephant staging area on New York Avenue, may want to charge his car wash to the circus.