Federal mediators will meet today in Minneapolis with eight grain companies and their elevator workers in an effort to end a month-old strike that has blocked Great Lakes grain shipments and caused a massive transportation snarl throughout the Midwest.

The strike, which began July 6, has shut down the huge terminals at Duluth and Superior that handle 10 percent of the nation's grain exports and also supply wheat to mills in Buffalo, center of the flour industry.

Agriculture Department officials said that Buffalo mills have been hiring rail cars at extremely high rates to carry wheat from the Midwest and that, eventually, these costs could be passed on to East Coast bakers.

The strikers are the 520 members of the American Federation of Grain Millers who operate the grain spouts, t im the holds of the loaded vessels and perform other jobs at the lakeside elevators.

The union is seeking a cost of living adjustment clause in a new three-year contract. Earlier, it rejected an 8 percent annual pay increase without a cost of living escalator.

The companies that are fighting the demands are Cargill, Continental, Peavey, Archer Daniels Midland, General Mills, International Multifoods, Conagra and Grain Terminal Associates, a farmers' cooperative.

As of last Friday, 1,700 railroad hopper cars were waiting to discharge grain. Management personnel were working to unload the cars so that they could be returned to areas where grain already is being stored on the ground for lack of transportation.

"We're paying a hell of a price for this," said Davis Helberg, Duluth port director. He estimated that the Duluth area is losing $500,000 a day.

Federal officials said the heaviest losers are Midwest farmers, who may already have lost tens of millions of dollars as a result of a transportation drisis that has been worsened by the closing of the big port outlets.

Many Midwest elevators are already full and connot accept more grain from farmers because there aren't enough rail cars to move what they already have. As a result, prices paid these farmers for their wheat, corn and soybeans have declined by 50 cents to $1 a bushel in the last 30 days.

In effect, trading firms have sharply discounted grain in affected areas while paying more where transportation is available.

Overall, U.S. grain exports exceeded # a record 100 million bushels a week three times in the last month, in response to strong foreign demand.

Most of this grain has been seiling out of the Gulf of Mexico, the Pacific Northwest, the East Coast and Great Lakes terminals at Toledo, Buffalo and Saginaw, which are not struck.

The Duluth-Superior complex traditionally serves wheat, oats, barley and sunflower growers in the Dakotas and Minnesota, and recently has become an outlet for corn and soybeans from southern Minnesota and Iowa.

Grain companies have been shifting to barges to divert shipments from the struck ports. But last Friday, upper Midwest farmers were dealt a new blow when a barge carrying scrap iron sank in the main Mississippi River lock number 26, at Alton, Ill., severely slowing the movement of grain from Milleapolis to New Orleans. An auxiliary lock is reported still functioning.

The Minneapolis area, a major grain collection point, received 2.700 fewer railcars in the first six months of 1979 than in the like period of 1978. "Some elevators haven't seen three cars in 90 days," said Bob Swanson, spokesman for the Minnesota Department of Agriculture.

Further congestion is expected when the harvest of spring-planted wheat starts in September.