The idea of building a skateboard park in Alexandria was born last fall when James H. Carrinton, an associate professor at George Washington University, ran out of actual small businesses to assign for study by teams of students in business research method.

"So I created a hypothetical problem," said Carrington, recalling he had talked to someone the previous summer about a skateboard park that had been built in Ocean City, Md.

The project he assigned to two of his students (he says he doesn't remember who they were) was to determine: "Is it economically feasible for a group of investors to construct and manage a skateboard park in the greater Washington area?"

The students' report was so encouraging, Carrington said, that he discussed the idea with several construction firms. He managed to interest Gordon Rudd, head of National Construction Co., a firm that built the White House swimming pool, many swim club and municipal pools in the area and polar bear cages at National Zoo.

Last week, the Alexandria Planning Commission approved the plan of a corporation formed by Carrington, Rudd and an accountant to build a skateboard park on the south side of Wheeler Avenue near the end of South Early Street.

If approved by the City Council, which will consider it Saturday, the park, costing about $100,000, would be built in four to five weeks and provide space for as many as 100 paying skateboarders at a time, according to Carrington and Barbara Rudd, Gordon Rudd's wife.

The city's zoning staff noted in a report that police have had problems recently with children skateboarding in streets as the sometimes dangerous fad has taken hold.

But the project has encountered opposition from residents near the planned skateboard park who say they fear it would be noisy, attract "undesirables" who would hang around after closing hours and create parking problems.

Fairfax County recently approved a skateboard facility, near Springfield Mall, and Carrington said one exists in Gaithersburg.

Carrington said the Alexandria skateboard park, with areas for beginners and experienced skateboarders, would emphasize "skill and recreation . . . analogous to figure skating," rather than "speed, danger and thrills . . . analogous to downhill racing and skiing."

According to Mrs. Rudd, it would have "bowls, waves, hills and swells of different sizes."

Customers would be required to wear safety equipment including helmets, gloves and knee and elbow pads. A "pro" shop at the site would sell or rent to beginners.

Carrington's son Timothy, 22, would be the manager. National Construction owns the land.

Washington area stores that sell skateboard equipment report the demand is high.

Fern Mathews, an assistant manager at landmark Shopping Center's Sears, Roebuck store, said the boards are selling "exceptionally well," and that manufacturers are from four to six weeks behind in filling orders.

Carla Sonntag, manager of the Sport and Hobby Warehouse at Springfield Mall, said her store is finding that skateboard accessories, such as wheels, nuts and bolts, are selling well. "Any skateboard park will do well," she predicted.