VLADIMIR KAGAN'S furniture looks like his name sounds - sleek but sumptuous. You could imagine his furniture in a setting for Greta Garbo, an Afghan hound curled at her feet.

For 30 odd-years Kagan has been known for his custom-designed, exquisitely constructed, very expensive furniture. His designs are manufactured in his small factory with its 30 skilled craftsmen in Long Island City. They are sold "to the trade only" - through archietects and decorators in his six showrooms across the country.

His designs - beginning with one of his best, his stylied logo - are quite original, though influenced by the art moderne period between the wars and the Bauhaus. To the pared down, ornamentless modern idiom, he adds the softness of curves, the elegance of deep channel upholstery, the lavishness of exotic fabrics, and sometimes visual tricks of varying success such as see-through bases.

Among his innovations are lucite bases for furniture, often lighted; tubular ceiling lighting and lamps; and his Omnibus multi-level seating systems which work something like a trundle bed. Probably his most dramatic design is the "tongue" chaise, extending out in a seeming cantilever, actually supported at the center by a Plexiglas base. The tongue chaise sells, through designers, for about $1,490 plus fabric.

For the first time, he has designed a less expensive "Multiples" series. The seating system, dining table and chairs are mass-manufactured by Previews of North Carolina. The line is being introduced this season, to be carried by department and furniture stores, locally by W & J Sloane.

Kagan will speak in Washington on Wednesday at W & J Sloane's interior design seminar at their new White Flint Interior Design gallery (reservations necessary). His recent design seminar at the American Society of Interior Designers convention here was standing room only.

In the summer on Nantucket, Kagan is far from the image his furniture might project of him. To hear his wife, Erica Wilson, tell it, he's more likely to be found underneath his Model T Ford, covered with grease, trying to find out one more time why the dratted thing won't go.

He's a sturdy-looking man with much wavy hair, thick Russian eyebrows, a quick and friendly smile, capable-looking hands and a disarming manner.

"When I have my needlework seminars at our cottage on Nantucket, he's in charge of entertainment the husbands," said Wilson, who writes about needlework in books and a newspaper column and teaches needlework on public television.

"It isn't too bad," said Kagan, who has helped put together Wilson's multiple needlework interests. He himself has taught a course in needlework for men at Cooper-Hewitt Museum in New York City. His furniture-showroom manager, Norbert C. Ratliff, admits: "He's often hard to find. He's always off somewhere with needlework."

The Kagans, who have three children, spend the winters in New York City, convenient to his drafting board and her needlework shop. In the summer, they move to their cottage in Nantucket, where she also has a needlework shop and runs seminars.

In his Nantucket summers, Kagan has found that husbands of needleworkers are often more interested in his alternate pursuits. "I said (to the husbands), 'I have this Model T and it's been laid up for a year.' The husbands and I all wnet out to the garage and looked at it. One is an engineer and he remembered just the thing to fix it. I spent the summer deep in grease. It's a lovely condition.

"Last week, the seminar members went on a clambake with us - the 31 ladies on the bus, the six men with me. The Model T caught on fire on two cylinders. It was spouting flame. We finally put out the fire and had it towed home."

Kagan also has spent quite a bit of time fixing the holes in his boat. "It was worth it," he said, "we won the race."

Kagan is as good with his hands at building furniture as he is at working on his antique transportation systems. "I have worked in my factory at every bench. I went into my father's factory when I was still in school. I know how it is all done. And when I do a new design, I still go into the workshop and follow it through.

"One of the strongest influences on design today is the lack of craftsmen. We're in a pickle in New York with the shortage. We once could get enough trained craftsmen from Europe. Refugees were our backup.

"In this country, craftsmen can make $10 an hour on the General Motors production lines. In our factories we pay only about $7 to $10 an hour - after they have spent 10 years in training. You can't find young people willing to do that.

"That's the reason you see so much upholstered furniture today. Upholsterers need less training than woodworkers - and they're paid less. The future is stamped out for us - good design but mass produced. I'm glad to say, mass production is getting better and better."

Kagan thinks that today there is a deep gulch between art furniture made by artists/craftsmen at one end - "all the Little Wendell Castles graduating from the Rochester School of Design" - and massproduced furniture. "There isn't much in between, where we used to be - custom furniture at wholesale prices that would still take a decorator's mark-up."

In the '50s and '60s, Kagan did marvelous pieces of furniture with carved-wood sculptural elements. "But we can't do them anymore. Too expensive. No craftsmen. I like to do more architectural pieces - cantilevers, patterns from skyscrapers, a bit brutal but good. Now I've had to to go to a more fluid design, soft looks, upholstery. Light, mobile furniture.

"I often do an entire room as a soft sculpture, an interior landscape. You don't have to have pull-up chairs. You can have stationary furniture. In our apartment in New York, we know we always want to sit in front of the fireplace and facing the view. It's possible to make commitments to sit in certain directions. Today, when we can't affort generous space, built-in furniture works best."

Kagan studied architecture at Columbia - "I lament not going to Harvard Business School" - and then went int o his father's furniture factory because his father "needed his son. I had to invent ways to do things, after hassling with my dad on how to do them."

His father, Illi Kagan, was a Russian refugee who had immigrated to Worms on the Rhine, set up a small factory and two shops that carried exquisite modern silver and rugs. "He designed modern furniture before World War I." He had gone to Germany first as a Germany POW in World War I and married a German woman. In 1938, the family was expelled "more I think because we were Russian than because we were Jews." And they came to the United States, with only his father's woodworking tools as capital.

The father first worked in New York in a furniture factory for $12.50 a week, while his mother rented rooms. Later he started doing repair work and then began making Bauhaus-style furniture. After a terrible time with an employer who did him our of $140 - a fortune then to an emigre - the elder Kagan was able to establish his own factory. In his later years, he was a sculptor, working mostly in wood, making cut-out designs.

The son opened a shop on 57th Street in New York City in 1949, with a $20,000 loan. "The design trade boycotted me, because I sold my own furniture to customers. I had to give up my shop and move to a showroom." At first Kagan did many interior design jobs, but "now I can only afford to do two a year. They take so much time. But I find it difficult to design in a vacuum. Most of my designs have been a collaboration with clients."

For a designer, Kagan doesn't change his own digs much. "Erica moves furniture around. I don't, once I'm convinced I like it a certain way. My furniture, I like to think, is elegance with tranquility, casual, keyed down. I like to pull furniture away from the wall."

Their sprawling 10-room cooperative apartment on Manhattan's Upper East Side is pretty much the same as it has been since he redecorated it in the early '70s. "They don't have time to redo it, anyway," said Ratliff. About that time the Kagans brougth over many English antiques Wilson inherited from her family. Kagan mixed his own modern designs with the English antiques and Wilson's needlework in the eclectic manner that was just then becoming the thing to do. The result is a comfortable, cluttered, contemporary cave dwelling.

In the beamed-ceiling living room with its carved wood and marble mantelpiece is a handsome carved cabinet and a sofa table with marvelous clawing feet. His 1950 rocker is covered in a Wilson needlework cover. The seating group with its extended chaise (strewn with Wilson pillows, of course) is from the 1970s. A huge Frank Stella painting with semi-circles of color dominates one wall. A less assertive painting by James Suzuki hangs over the fireplace. Best of all is the great yellow Indo-birdcage, another Kagan design. The room also boasts a marble nude, plants, African carving, oriental rugs, a Kagan glass-topped table and a clavichord. The marble fireplace mantle holds an art nouveau vase.

The warm dining room has even more of the Wilson inheritance - a vast Welsh dresser displays their pewter collection. A Renaissance chest is from the Wilson's London home. A refectory table made from two ancient bedsteads opens up to 12 feet. Kagan's chairs and cylinder lighting fixtures are new. There are screens to cover the windows instead of draperies. The door is highlighted with white paint outlining the panels. Shelves hold all sorts of china and glass collections.

In Nantucket, their cottage holds mostly antique furniture, much of it Victorian. The effect is country and casual. Built-in cupboards hold the china. Still, the candlesticks drip with crystal and the flower arrangements are obviously not only the result of much thought but also serve as inspirations for Wilson's needlework.

Kagan said of his needlework, "I learned how to do it in self-defense. Erica had this big job to do to be published in House & Garden. She couldn't possibly do it in time, so I had to learn needlework to help."

On her designs and her writings, Kagan acts as devil's advocate. "I figure if I can understand it, anyone can." He doesn't offer her the same privileges with his work - "She's a great distraction." Sometimes, though, by request for a custom design, he has made furniture for a client with needlework by Wilson.

Kagan has helped illustrate her books and given financial advice on her expanding needlework empire of kits, shops, and now their tours of needlework in private European mansions. They're planning five weeks in Europe, a week in her family's home (between renters) in London, then castle-hopping, hunting needlework in Scotland and England with 35 tour members. Next year they'll lead a needlework tour to France. The Kagan children - Illya, 9; Vanessa, 11; and Jessica, 20 - often go along. None of them have any interest in needlework, according to their father.

His interest in her needlework career comes not from any great financial talent. "We're not that business-minded. Neither of us is good at numbers. We thought the inventory in the needlework shops was about $200,000, and after a six-month management team survey, we found it was $350,000."

Not content with the needlework, the furniture, the boat and the Model T, Kagan said, "I long to own a restaurant. I have such a tingle of happiness when I'm cooking.

Who knows, maybe we'll walk down a Nantucket road some day, stop where the Model T is parked and there will be this exquisite restaurant, with elegant furniture covered in needlepoint, Erica Wilson handing out menus and Kagan under the chef's hat in the kitchen.