Washington Post Staff Writer

Americans across the country seem to be booking earlier this year for their summer holidays at the beach or in the mountains. In fact, travelers who don't make reservations soon may not get the place of their choice.

No one knows for sure why the rush is on for reservations, but the speculation is that many Americans who flocked to Europe in the past three years have decided to stay home. The dollar no longer is the strong incentive it ws to go abroad, and terrorist incidents have raised concerns about the safety of foreign travel.

At two popular beach resorts near Washington, summer rental agencies said they were caught by surprise by the volume of business so early in the season.

January ''was like the middle of July down here,'' said John DeRosa of Martin Groff Real Estate & construction Co. of Ocean City, Md. ''Everyone wants to make sure they are reserved.''

''It seems like we are busier,'' said Alma Ashley, rental manager for Anderson-Stokes in Rehjoboth Beach, Del., ''and that reservations came much earlier this year. We've been renting since Thanksgiving.''

While DeRosa and Ashley are far from being sold out for the summer, they said that choice lodgings, including beach-front places, are getting hard to find. This is particularly true for the first two weeks in August, the height of the beach holiday season.

The rate for a two-bedroom, sea-view condominium apartment begins at about $625 a week in prime time at the Maryland and Delaware resorts. A similar apartment facing inland to the bay begins at about $450.

A similar rush seems to be happening farther up the coast at Cape Cod in Massachusetts, another popular destination for Washington vacationers. ''January was incredible,'' said Audrey Sherwin of Chequessett Village Real Estate, who has been phoning up her regular Washington-area clients to let them know that rentals in the Cape Cod Bay town of Wellfleet are going fast.

Many of her renters, she said, are lawyers who are among the 10,000 attorneys who last year traveled to the American Bar Association Convention in London on their vacation and who sent their friends, instead, to Cape Cod. This summer, the lawyers are returning to the beach (their convention is in New York City), but now so are their friends.

In Wellfleet, a two-bedroom house away from the beach rents for about $550 a week in August; a beach-front house goes for about $1,200, though by now they are very scarce.

Other popular summer resort areas are experiencing unusually heavy advance reservations. ''We're definitely feeling it here,'' said Lynn D. Ailes, a sales manager for Grand Canyon National Park Lodges in Arizona.

''Our advance reservations picked up earlier this year than expected. By January, we were swamped. We were getting many, many more phone calls per day than last year.''

She has available about 1,050 rooms in seven lodges at or near the southern rim of the Grand Canyon, so space usually can be found for last-minute travelers, but they might not get the exact dates they want or the lodge they prefer.

The two most charming places to stay at the canyon are the two older lodges, Bright Angel Lodge and the El Tovar Hotel, both offering rooms right at the rim. Bright Angel offers comfortable cabins for $45 a night for two people; the El Tovar is a luxury hotel where the rates range from $90 to $105 a night.

The biggest crunch at the Grand Canyon is for saddle space aboard the famous mules that carry sight-seers deep into the canyon on winding, precipitous Bright Angel Trail. Twenty mules descend daily on a seven-hour round trip to Plateau Point overlooking the Colorado River. Another 20 miles continue on a 10.5-mile trek to the bottom of the canyon, where riders spend the night in modern cabins at Phantom Ranch right on the river.

By mid-February, almost all the June mule trips already had been booked, said Ailes, ''and July is going fast.''

One of the country's most popular family destinations, Walt Disney World and Epcot Center in Orlando, Fla., is also reporting heavy bookings for the three hotels it owns and operates: the 1,050-room Contemporary Resort Hotel, the 860-room Polynesian Village Resort and the 300-room Disney Inn.

Normally at this time of year, the Disney hotels would be booked only through March, ''and you would see a awakening after Easter until summer. But this year we're solid right on through the summer,'' said spokesman Bob Mervine.

He doesn't mean you won't find a place at Disney World, but if you plan to visit during the summer now is not too soon to assure yourself of a reservations if you want to stay at a Disney hotel. Rates for two begin at $95 a night at the Disney Inn, $115 at the contemporary and $120 at the Polynesian.

There are six other privately operated hotels at Walt Disney World Hotel Plaza in Lake Buena Vista with 3,000 rooms and dozens of other lodgings in all price categories throughout the Orlando region.

American cruise Lines of Haddom, Conn., which offers spring-through-summer cruises on small ships in the Chesapeake Bay and along the Atlantic Coast from Florida to New England, also is reporting ''heavier than normal advance bookings'' for its spring and summer 1986 voyages.

American's president, Charles Robertson, attributes the demand to the declining value of the U.S. dollar abroad ''and traveler apprehension that continued international instability may pose threats to personal safety and security.

''Many of these travelers who might otherwise be cruising the Mediterranean next season will instead be rediscovering America in the safety of our own waters," he said.