Union and management in the specialty steel industry joined yesterday in asking the government to extend a soon-to-expire import quota program for another three years, thereby handing the administration a new weapon in its war on inflation.

The administration has said it will use its leverage over imports as part of a carrot-and-stick strategy for winning voluntary compliance with its anti-inflation guidelines, and the specialty steel request appears to fall within the reach of that strategy.

This puts United Steelworkers President Lloyd McBride, who takes a dim view of both imports and the administration's wage guidelines, in an awkward spot.

Like other union leaders, McBride has major problems with the proposed 7 percent ceiling on wage and benefit increases and said yesterday that "special circumstances" may require settlements in excess of the government's limit in some cases.

But he emphasized that the union is giving the guidelines "very serious consideration." Asked if the union's lack of full support for the program may jeopardize the imports request, he said he hoped the issue would not be decided by "retaliation."

On the industry side, Richard P. Simmons, president of Allegheny Ludlum Steel Corp. and chairman of the industry advisory group, said his company will abide by the guidelines, although he couldn't speak for the other 19 companies involved in the importcurbing request.

While contracts in the basic steel and specialty steel industry do not expire until 1980, the union will be renegotiating contracts covering about 150,000 other workers during the next year.

The request for the quota extension was filed with the International Trade Commission, which has 90 days to make a recommendation to President Carter. The quotas will expire June 13 unless extended by the president.

The quotas were granted by President Ford in 1976, setting specific limits that allowed imports to rise by only 3 percent a year after a first-year rollback of 6 percent, according to Simmons. Imports now account for about 11 percent of the country's 1.7 million ton consumption of stainless steel and other specialty steel products, down from about 18 percent before the quotas were set, Simmons said.

If the quotas are allowed to expire, said Simmons, "we will once again be defenseless against the kind of unfair competition which we faced so often in the past -- competition from government owned or subsidized foreign specialty steel companies who do not have to meet our disciplines of profit and capital formation."

The "threat of unfair imports" is greater now than it was before the quotas were set, he added, noting that Britain, Finland, Brazil, Mexico, Spain, Korea and other countries are expanding production capacities for export purposes.

McBride said an end to the quotas could jeopardize roughly 25,000 steel-worker jobs, just as it did in the 1974-75 period when unemployment reached nearly 45 percent in many communities with specialty steel plants.

"While the disorder and devastation caused in large measure by the imports have been arrested, full recovery has not yet been effected," said McBride, adding "short-term gains in employment and in production and profit levels could very well be wiped out" without quotas.

Simmons said the quotas increased employment, profits and expenditures for research and development while cutting costs. "The restraints, he said, "have not proven to be inflationary."

Specialty steel accounts for only 1.5 percent of domestically produced steel tonnage and 9 percent of the dollar volume of steel shipments, but it is considerably more labor-intensive than other forms of steel production.