A group of domestic shoe manufacturers yesterday asked the International Trade Commission to impose five years of quotas on foreign shoe exports to the United States.

The restrictions are needed to halt the rapid decline of U.S. shoe companies, 105 of which went out of business in 1984, the shoe makers said.

Last year's closings of domestic shoe plants were double the number of American shoe factories shuttered in 1983. And at least 15 of the remaining 300 U.S. shoe manufacturers have closed or have made plans to stop production in 1985, industry representatives said.

The request for quotas comes nearly one year after the ITC ruled that imports caused no harm to the U.S. shoe industry. But domestic shoe representatives argued yesterday that the ITC used erroneous data and misinterpreted other information in reaching that conclusion.

Nonrubber footwear imports now account for 71.5 percent of all shoes sold in the United States, up from 63 percent in 1983. The quotas proposed by the Footwear Industries of America would limit the import share to 55.2 percent of the domestic shoe market for each of the five years the restrictions would be in effect.

The quotas would fall most heavily on medium-priced and expensive shoes exported to this country. Lower-priced shoes would be allowed to come in at higher levels "to ensure minimal impact on low-income consumers," FIA representatives said in presenting their proposal.

"Our difficulties are directly attributable to imports -- those that continue to flood the U.S. market and those that are being held in inventory," said Richard W. Shomaker, president of St. Louis-based Brown Shoe Company, the largest producer of nonrubber footwear in the United States.

Brown said that his company has closed plants, cut employment, dropped certain product lines and improved automation to remain competitive. But even with those moves, Brown's after-tax earnings in 1984 fell 50 percent from the previous year, mostly because of "intense price competition from imports."

Brown was one of nine people to speak yesterday in favor of the proposed quotas during the first of three days of hearings before the ITC. Shoe importers also will appear before the commission.