Shaken by the inability of several nations to pay their foreign debt this year, Western banks today signed an agreement with Poland rescheduling most of its 1982 debt.

The agreement, covering $3.4 billion in commercial principal and interest owed by Poland this year, was more lenient than the first rescheduling arrangement concluded with Poland last year. It also included a new provision that the banks would recycle about half of Poland's interest payments in the form of new trade credits.

This seemed to reflect Western bankers' recognition of Poland's worsened financial predicament as well as their eagerness to recover at least some of their money from the troubled Communist state.

Breaking precedent, the banks decided this year to negotiate an accord with Warsaw authorities before Western governments -- also heavily invested in Poland -- even have begun talks on an official 1982 debt of nearly $6 billion. Banks last year waited for the governments to reschedule, but this year Western governments froze the talks in retaliation for the imposition of martial law last December.

The new restructuring agreement was signed at a closed-door ceremony in a Vienna hotel by senior members of the Warsaw goverment and the Polish national bank Handlowy and officials from leading banks representing Poland's 503 Western commercial creditors.

Under the terms of the accord, 95 percent of the $2.3 billion of principal will be repaid over 3 1/2 years after a four-year grace period.

Like the 1981 agreement, which allowed Poland to roll over $2.4 billion in bank debt, the new deal sets interest on the deferred principal at 1.75 percentage points above the floating London interbank lending rate -- the cost of obtaining funds in London money markets -- plus a 1 percent rescheduling fee. Poland is obligated to pay the remaining 5 percent of principal before the end of this year.

In a major departure from last year's rescheduling model, the Western banks agreed to recycle, in effect, half of the additional $1.1 billion in interest that Poland owes this year.

Warsaw is committed to paying back the interest in full in three installments by early next year, but $550 million of this will be relent by the banks in the form of fresh short-term trade credits maturing in three years. Previously, the banks had required the Warsaw government to meet its interest payments without any provision for new credits.

A senior Western banker, who asked not to be identified, said this recycling measure will enable Poland to afford continued imports of items needed to produce exports. These exports, in turn, will earn new hard currency which Warsaw can use to pay its debts to Western banks and governments, the banker argued.

Although the recycling provision is a significant concession, Polish authorities, using the implied threat of a moratorium on debt repayments, initially had hoped for more. When negotiations began in the summer, Warsaw asked for a rollover of 80 percent of the interest due and a 10-year deferral of the principal.

Both sides appeared bent on not yielding much ground during the talks, until about the time that Mexico--whose bank debt of nearly $60 billion dwarfs Poland's total Western debt of $25 billion--started looking shaky, as well.

"The Poles got a better deal this year for two reasons," said Jan Vanous, an East European affairs expert with Wharton Econometric Forecasting Associates in Washington. "One was the realization on the part of bankers that there was little chance of a turnaround in the Polish economy. But the major reason was the development elsewhere in the world of national debt problems that caused Poland's to fade away in comparison and made bankers eager to wrap things up with Warsaw."

Vanous was critical of Western governments for holding back on rescheduling in the name of sanctions against martial law.

"The banks have actually taken a tougher line than the governments by forcing Poland at least to service some of its commercial debts," he asserted. "What effectively has happened is that the governments, by refusing to negotiate, have rescheduled 100 percent of the principal and interest owed them."

Western governments made no public criticism of the bankers' talks, and an informed source said he knew of no behind-the-scenes government pressure to block the rescheduling. The Reagan administration has resisted calls to declare Poland in default, suggesting some concern within the government about the world financial repercussions of too tough a position against Poland.

The need to make some immediate payments to Western banks is contributing to the sharp curtailment of Poland's imports from Western countries this year, reported Washington Post Correspondent Michael Dobbs in Warsaw.

This has meant a drop in production, creating a downward spiral. Imports from capitalist countries dropped by 30.3 percent over the first nine months of this year. This was the main factor behind a 5 percent drop in production during that period compared with the same stretch of time last year, the fourth consecutive annual drop in Polish industrial production.