A Mississippi group has beat out 300 competitors - most of them based in New York, Los Angeles and other big cities - to win the contract for a major cultural-exchange exhibit that will tour the Soviet Union.

"This is the first time we have chosen a design group from the South," said Ron Underwood, project director for the U.S. Information Agency, the government office sponsoring the exhibit.The exhibit, called Design USA, will be produced by Yoknapatawpha Exhibit Group, USIA officials announced. The group is a joint venture of two Jackson firms - Communication Arts Co., a graphic design and media production studio, and Mockbee-Coker-Howorth Architects.

The exhibit will showcase U.S. architecture, product design, graphic design and design education. It will tour nine Soviet cities in 18 months, starting in Moscow next June.

In its proposal, the group emphasized its Mississippi background. Yoknapatawpha is the fictional Mississippi county that was the setting for several works by Nobel Prize-winning novelist William Faulkner.

Jeanne B. Luckett, vice president of Communication Arts, noted the group's experience with the Mississippi pavilion at the New Orleans World's Fair. She said the challenge there was to sell the attributes of a state that is often stereotyped and misunderstood.

Design USA is the second traveling USIA exhibit to result from the 1985 cultural exchange agreement between President Reagan and Soviet General Secretary Mikhail Gorbachev. The first, which is touring the Soviet Union now, deals with communications.