The United Rubber Workers, whose contracts expire at 12:01 a.m. Saturday, epitomize the problems of blue-collar unions in the nation's old manufacturing industries.

The problems include a deluge of foreign imports; relocation of plants from northern labor strongholds to the South; rapid technological change, and a structure of labor-management relations ill-suited to today's global economy.

Tire makers , who compose the core of the union's strength, have declined in number nationally from 83,000 in 1969 to 77,450.

Akron, once the "tire capital of the world," and still the headquarters of four of the five largest U.S. rubber companies, no longer makes automobile tires.

Goodyear and Firestone closed their Akron passenger tire plants last year. As a result of these shifts officals at URW headquarters-a red-brick relic in downtown Akron marked by a neon sign-are struggling against heavy odds to readjust.

Labor-management relations in the rubber industyry traditionally have been acrimonious. Even today, after nearly a century of technical innovation, labor is still a major cost in making tires, rubber soles and other products. Therefore, the stakes for the companies have always been high in labor disputes,

Company officials say that high wages and burdensome work rules obtained by the unions over the years were responsible for the exodus of plants from Akron.

In the aftermath of a 4 1/2-month-long strike in 1976, Goodyear Chairman Charles J. Pilliod accused Akron workers of having a "bad attitude" and an "owed-something feeling."

For their part, union officals charge the companies with a callous disregard for employes who gave a lifetime of service in the old, northern plants.

However, beyond the deeply rooted hostilities are fundamental economic facts that have played a major part in the weakening of the URW.

One major factor has been the rapid switch to radial tires, a shift that caught the major U.S. companies unprepared and contributed to the United States becoming the world's largest tire importer in less than 10 years.

In the 1960s, the major automobile companies in Detroit resisted putting radials on their new cars. Radials last twice as long as conventional "bias ply" tires, and give better gasoline mileage because of their internal construction.

But as steel-belted radial tires were popularized in Europe in the 1960s, Detroit resisted them. Raidals gave a somewhat rougher ride and, being more expensive than conventional tires, added to new-car prices.

The result was that when American motorists began demanding radials after 1973 for reasons of fuel economy, the U.S. companies could not supply the market. Imports filled the gap.

Sales of imported tires, led by France's Michelin, which pioneered radial tires, are running at $1 billion a year. Imports cover 10 percent of the U.S. market compared with 3.4 percent in 1969, and have increased from 4.5 million tires a year then to 17 million a year now.

Added to the threat to northern blue-collor jobs posed by imports are the job losses caused by the migration of plants to the South-a shift that the URW has not been able to keep up with. The number of workers covered by the URW's 1976 contracts with the four major firms has dipped from 61, 300 to 54,800.

Most of the 14 major North American tire plants that are not organized are in the South.

Company officials acknowledge that lower Southern labor costs and higher productivity are a major reason for the relocation. Goodyear's current expansion program involves a new, highly automated radial tire plant in Lawton, Okla., and expansion of plants in Alabama, North Carolina and Tennessee.

While truck tire plants in the northern United States have been closing, Michelin has steadily expanded the nonunion work force at its radial truck tire plant in Nova Scotia. Most of the company's increased output of tires is exported to the United States, even though the U.S. government imposed countervailing duties on Michelin imports in 1972.

URW efforts to organize Michelin in Nova Scotia have failed so far. Workers at the plant at Granton voted by nearly 2 to 1 against URW representation.

Despite the bleak situation facing industrial workers in the northern United States experts see several encouraging signs. One is that labor costs are rising faster in Europe than in the United States.

Michelin has invested more than $1 billion in new tire plants in the southern United States since 1972-in part because of the attraction of a non-union work force.

Also, there are some signs of increased militancy among workers in less-developed countries, a development that could bring foreign labor costs closer to those in the United States.

One company bucking the trend is General Tire. Recently workers at its Akron truck plant accepted a pay cut and longer work week to keep the plant going. CAPTION: Picture, Akron headquarters of Firestone Tire and Rubber Co. The company no longer makes automobile tires in Akron, once the "tire capital of the world." AP