Behind the screen, busy hands artfully maneuvered thin poles to manipulate the jointed figures formed from rainbow-hued pieces of plastic.

Before the screen, more than 100 youngsters watched delightedly yesterday as striped zebras, spotted leopards, magnificently garbed African warriors, elephants and engaging birds flitted in silhouette across the illuminated screen.

One of the regrettable disruptions by Washington's Blizzard of '79 has been that of the Shadow Box Theatre which, on a visit from New York City, has had to curtail its performances at the Smithsonian. The stand will close with two public performances today and two more tomorrow.

For those who think of puppets either on strings or on the hand like a glove, shadow puppetry is a delightful new find with the charm of an animated cartoon.

If you have ever placed your hand in front of a light to cast a shadow figure on the wall, you have an idea of the basic technique. In shadow puppetry, silhouettes are thrown on one side of an illuminated screen and viewed by the audience from the other side.

As the legend goes, shadow theater dates back 2,000 years to China. Han Emperor Wu-ti, we are told, lost his favorite concubine and commanded the court magician to summon her back.

The crafty magician, with his life at stake, devised a technique to cast the silhouette of Wu-ti's true love on a screen. The emperor -- who, of course, had other concubines -- was satisfied with her shadow.

The Shadow Box Theatre has combined the ancient shadow theater technique with old African folk tales, traditional African music, and authentic African musical instruments in its show, "The Story Drum."

Within the framework of one African tale -- the story of a little girl, Kijana, who is kidnaped by a Zimwe (African bad man) and imprisoned in a drum to sing stories -- the Shadow Box Theatre tells three other tales about how the animals got their colors, how the turtle got his shell, and why the egret flies free.

Live characters -- the mother and father -- talk to the animated puppet shadows and also enlist the help of the audience in calling for the daughter.

Today there will be two shows at 11:30 a.m. and 2 p.m., and the same schedule tomorrow. The performances are given in the Discovery Theater in the Smithsonian's Arts and Industries Building. It's a theater with carpeted steps, so youngsters can sit or sprawl in comfort whilc watching the show.

Tickets are $2.25 for adults and $1.75 for children. Reservations should be made by calling the Smithsonian Box Office.