Charging that rodeos constitute "an orgy of animal abuse," a coalition of humane societies and animal rights groups is planning to demonstrate against a special rodeo exhibition being staged at the Capital Centre this Saturday for President and Mrs. Reagan and 8,000 White House guests.

The affair is by invitation only and is organized by the Professional Rodeo Cowboys Association as a "salute to the American government." The show is particularly galling to the humane groups because it features prominent members of the Reagan administration, lending the presidential imprimatur to what the groups consider a cruel sport.

The head of the Humane Society of the United States, a group that has opposed rodeo for nearly two decades, wrote Reagan this week to urge the nation's First Rancher, ex-star of horse operas and afficionado of custom-made cowboy boots, not to attend the presidential performance where the competitors will include Commerce Secretary Malcolm Baldrige and Pete Clark, son of National Security Adviser William P. Clark.

"Rodeos result in torment, harassment and stress being inflicted upon the participating animals . . ." wrote John A. Hoyt, president of the Humane Society. "Such callous disregard of our moral obligation towards other living creatures has a negative impact on society as a whole . . . . "

The coalition, which includes local chapters of the Society for the Prevention of Cruelty to Animals, People for the Ethical Treatment of Animals and the Humane Society, plans to picket outside the Capital Centre while guests of the White House file in.

A White House spokesman said President Reagan intends to attend the rodeo and would not comment on the issues raised by the animal protectionists.

Saturday's 2 p.m. exhibition is a special showcase for top cowboys gathering at the Capital Centre to rope calves, ride bulls, and display other traditional skills in the three-day "World's Toughest Rodeo." Prize money totals $45,000.

Humane organizations and rodeo organizers have been debating the cruelty issue for years. Both sides cite studies by veterinarians and researchers to support their contentions. The humane groups condemn the practice of jerking calves to a halt with a rope about the neck, saying it causes injury. They charge that use of electric cattle prods to shock animals and flank straps to goad them into bucking are cruel.

"If people saw teen-agers chasing a dog and throwing it down on the ground they'd be screaming," said Bob Baker of the Humane Society. "The problem is that people don't relate to farm animals as they do to pets."

The Professional Rodeo Cowboys Association, which is the major rodeo organization in the hundred-million dollar industry, maintains that animals are treated according to "stringently monitored practices." Rodeo spokesmen argue that the conformation of vertebrae and muscle in a calf's neck protects it against injury from a cowboy's lariat, and that electric cattle prods and flank straps are not harmful to the animals.

"Statistics show there are fewer injuries to livestock in a rodeo than on a ranch," said association spokesman Dave Baldrige. "Rodeos can keep animals alive that otherwise wouldn't be. We have numerous animals that are still performing in their 20s and 30s."

The World's Toughest Rodeo attracted a few protesters when it played the Capital Centre for the first time in 1981. This year, along with press releases touting the final performance of Joe Kool, the legendary, 2,000-pound Brahman-crossed bull known as one of the hardest rides in the history of rodeo, the organizers have included a book called "Facts" that proffers the official rebuttal to charges leveled over the years by humane groups.

"Horses have survived for a million years because of their ability to buck and flee," says rodeo president Steve Gander, "not because some humane society put diapers on them."