They won't have sequined girls riding elephants or roustabouts raising the Big Top in the cold gray of morning. But the show coming to town next week will be circus-like all the same, with missles to pat, guns to aim and helicopters to climb around.

The sponsor is not Ringling Brothers, but a fraternity of military boosters called the Association of the United States Army. The association is selling display space at the rate of $8.50 a square foot to the who's who of the arms industry.

Defense contractors are so eager to hawk their weapons at this year's arms bazaar that the association reports a record number of exhibitors have rented space for the show Monday through Wednesday at the Sheraton-Park Hotel - 62 compared to 48 last year.

Gatling guns that can fire thousands of bullets a minute; "smart" missiles that can blow up any tank they can see, and squadrons of model warplanes plus a couple or real Army helicopters are among the wares to be displayed or portrayed in films shown in the mini-theaters spread around the basement floor of the hotel.

Even though nothing can be sold outright, the defense contractors feel they dare not miss these unusual bazaars sponsored evey year by the Army association, Air Force Association and Navy League.

"You're noted by your absence," explained a defense executive from a company that rented a big chunk of floor space at the Air Force Association convention here Sept. 20 to 22 and will be on hand again next week.

"YOu establish contacts, said Marvin Klemow, marketing director of the Israel government's aircraft company, in explaining why Israel rented space at the Air Force Association bazaar. "It had 20 minutes with Gen. Brown," he said, referring to Gen. George S. Brown, chairman of the Joint Chiefs of Staff.

Besides the contacts contractors make in talking shop in the cubicles and at cocktail hours during the shows, these affairs are being used by defense firms to extol the ways their weapons fit into national defense policy.

Boeing, for example, saw the Air Force Association meeting as this kind of opportunity. The company argued that President Carter made the light decision in choosing the B-52 bomber-cruise missile combination over the B-1 bomber.

Boeing built the B-52 bomber as well as the AIr Force's cruise missile. The company is also trying to sell its 747 civilian transport plane as a cruise missile carrier. A competitor, Rockwell International, builds the B-1 bomber. Boeing, at the Air Force Association meeting, reported to a Kukla, Fran and Ollie type of puppet show to make its pitch.

"Aren't the B-52s getting old?" Martha Lambert of Aniforms in New York asked the puppet standing on the stage in the Boeing cubicle.

Old! Old!" protested the Boeing puppet. "They're getting better. Even news." (The Air Force has spent million to renovate the B-52 bomber fleet.)

As for the cruise missile to go on the B-52, the puppet whispered conspiratorially to Martha that the weapon would drive the Russians crazy by throwing more cruise missiles at them than their defenses could handle.

"If I threw six balls at you," asked the puppet, "how many could you catch? Now, that, Sweetheart, is saturation . . . And we can expert fantastic developments in the future . . . Margaret. You catch my drift?"

The drift, as far as Boeing is concerned, is that the United States should buy so many cruise missiles that the Soviet defenses could not hope to knock all of them down if war came.

Other contractors at these bazaars try to persuade anyone who will listen that their weapons are the ones that provide the most bang for the buck. With more defense contractors than there is business, the corporate pitches have turned increasingly to puppet shows, card tricks and girls spinning a roulette wheel such were the scenes at the Air Force meeting last month. They will be duplicated, if not outdone, in some fashion next week as show business makes a return engagement for the arms makers.