Eastern Airlines today announced a consortium of 29 banks had agreed to relax the terms of lending agreements to allow it to continue on schedule with a planned $900 million aircraft purchase.

The agreement, which was reached last week, was the airline's latest step in effort to weather sharp downturns in passenger traffic at a time when fare-cutting competition is continuing to cut into profitability among the nation's major airlines.

It also followed by one day a sharp downgrading of a series of Eastern obligations by Standard & Poor's Corp., one of the nation's two major debt rating agencies, and kept alive concern among Wall Street analysts about the financial health of the airline industry.

One leading analyst privately calls the state of the airline industry "a depression," although most experts say Eastern's route structure is likely to insure its long term viability as long as it can weather its current mounting debt and sagging traffic.

"The company has been relatively expansive in its policies and they are very well situated in the long term," said Anthony Low-Beer of L. F. Rothschild, Unterberg, Towbin. "But getting from here to there could be a problem if the economy is too nasty."

Eastern recently reported that it lost $55.8 million for the first eight months of the year, up from losses of $8.9 million last year, although seat miles on Eastern routes were cut by about 7.8 percent in the first half of the year compared to last year.

In 1981, Eastern lost about $66 million.

But a combination of Eastern's route expansion effort into Latin America, picking up routes abandoned by bankrupt Braniff Airways, and its airplane purchases have raised its debt-to-capital ratio from an expected figure of 80 percent to 83 percent, up from 73 percent just four years ago.

In its announcement today, Eastern said it "received required consents" from the banks to "relax certain financial tests the airline must meet" through the end of 1982. "Receipt of the waivers will permit Eastern to proceed with the planned purchase of Boeing 757 aircraft as part of its fleet modernization plan," the airline said.

An Eastern spokesman said today that the airline expects to meet its obligation on its debt.

"The problem is that our books don't say what we thought they'd say," he said.

At stake immediately at the Miami-based airline is its purchase of 27 Boeing 757 stretch aircraft, which seat 185 passengers and are considered vital to the airline's capital expansion program.

The cost of each of those planes is about $35 million, according to Robert Joedicke, first vice president with Lehman Brothers Kuhn Loeb. Two of the planes are scheduled for delivery in December and another 13 are due next year.

The financing for the planes is expected to come from the equipment certificates and from drawing down a $400 million revolving credit line .

The $900 million financing package will come from about 100 financial institutions of varying descriptions, the spokesman said.