When Gennaro "Jerry" Angiulo and his brothers needed to do some banking, they often strolled into their neighborhood branch of the Bank of Boston here and plunked down paper bags stuffed with tens of thousands of dollars in cash.

The Angiulos, reputed ringleaders in the New England Mafia, often swapped pleasantries with the bank tellers and then exchanged their cash for cashier's checks -- transactions that, under federal law, must be reported promptly to the Internal Revenue Service.

Yet for a four-year period until 1983, the Bank of Boston has admitted it kept two Angiulo-controlled real estate companies on a special "exempt" list that allowed the brothers to carry out more than $2.1 million in cash transactions without having them reported to the government.

The failure of the Bank of Boston -- this city's oldest, biggest and most venerable bank -- to disclose its business with alleged mobsters is one element in an unfolding drama that has shocked this city's financial community and spurred a spate of federal and congressional investigations.

The bank's problems have been compounded by a public relations nightmare arising from incomplete disclosures and contradictory public statements, according to many financial analysts, government officials and banking experts.

"It boggles my mind," says James E. Moynihan of the investment firm of Moseley, Hallgarten, Estabrook & Weeden. "I've met with their top people and there's no doubt they're a first class operation. But I keep reviewing their press releases and statements and they just don't add up."

The story broke nearly a month ago when the bank pleaded guilty to a felony charge of "knowingly and willfully" violating the Bank Secrecy Act by not reporting more than $1.2 billion in cash business it conducted with a group of mostly Swiss banks.

These bank-to-bank transactions, which involved the shipment of unusually large amounts of $5, $10 and $20 bills to Boston in exchange for large $100 bills, suggested the Bank of Boston may have been used unwittingly as a conduit for illicit drug profits being laundered through Swiss banks, according to federal prosecutors and officials.

Yet after two news conferences by Chairman William Brown, in which he and other bank officials described the reporting problem as a mere "systems failure," the bank has not offered an explanation for why the violation occurred. It is a failure that seemed all the more puzzling last week after statements by Treasury Department officials that, as early as 1982, senior bank officials were warned by federal regulators about problems in its foreign and domestic cash reports.

"I can't explain it," said Wayne Taylor, the bank's official spokesman, when asked about the reporting violations last week. "There certainly do appear to be discrepencies. . . . We were in error for reasons we are still trying to get at."

The inability of the bank at this date to offer a more complete disclosure or to take disciplinary action against any of its employes has annoyed some federal officials.

"I continue to be amazed by the statements that come out of the Bank of Boston," said John M. Walker Jr., assistant secretary of the Treasury for enforcement and operations, in an interview on Friday. "I'm most skeptical of anything they say. They claimed initially they missed the notice in the Federal Register about the cash reporting requirement , but that raises more questions than it answers about the culpability of the bank.

"That regulation is not a complex one," he added. "This is a bank that has devoted considerable resources to their compliance efforts. They have a reputable law firm that represents them. . . . It's baffling. We're talking about gross mismanagement of the worst sort."

That all this has happened to the Bank of Boston in particular may be the most startling element of the story to people here. A towering symbol of Yankee rectitude with a history that dates back to the Revolutionary War, it has long been the preeminent New England bank. In sheer size alone, the bank dwarfs its competition; with more than $22 billion in assets, it is more than four times as large as its nearest rivals.

In the 1930s, it was one of the first American banks to become a major financier of Hollywood movies. Today, with some 15,600 employes, it is the only bank in the region with extensive international operations.

Yet its dominance also has contributed to its problems, breeding an insensitivity to public opinion that sometimes has soured its relationship with the Boston community, according to government officials and bankers.

Even before its recent travails, the bank was in trouble with some political and community leaders here for threatening to move its credit card operations out of state because the Massachusetts legislature had failed to lift its interest rate ceiling on credit card accounts.

"This institution is really in the Dark Ages when it comes to public relations," said the Bank of Boston official, who asked not to be identified. "This was always a banking monolith because we're the biggest. But there's a certain arrogance because of that. It's a viewpoint that says, 'We're so big, we can flex our muscles.' That's a part of the corporate culture here."

But even if no more than negligence by bank officials was involved -- a question that a federal grand jury is trying to determine -- it does not excuse the bank, according to federal prosecutors and Treasury Department officials. The reporting regulations that the bank failed to follow -- which since 1980 have required them to disclose all overseas cash transactions of more than $10,000 -- are now considered indispensable tools in the federal government's war on money laundering by international drug traffickers and organized-crime figures.

Five years ago, the government launched Operation Greenback -- a successful attack on money laundering in south Florida that netted more than 100 convictions of drug smugglers, many of whom routed hundreds of thousands of dollars in illicit profits through local banks, sometimes with the collusion of local bank officials there.

Patrick Walsh, a prosecutor who worked on Greenback and is now with the New England Strike Force on Organzied Crime, said he warned banks here to strictly comply with the reporting regulations -- or else.

"The banks sometimes say that filing these reports are technical and when they fail to do so it's negligence rather than criminal," said Walsh, who helped negotiate the plea bargain with the Bank of Boston and who now is investigating other banks in the region for reporting violations.

"But we view these as serious violations," he added. "It's not for them to make that determination. The law is there, and we expect them to pay attention to it. If they don't, we'll prosecute them for it.. . . When they don't file these reports, it's assisting people who are engaged in some very serious crimes."

The Bank of Boston vigorously denies that its dealings with Swiss banks offered such assistance. For years, a SwissAir flight would arrive every two to three days in Boston's Logan Airport carrying the small-denomination bills from Swiss banks with which the Bank of Boston has a correspondent relationship, according to federal prosecutors.

In his press conference two weeks ago, Brown described these as routine transactions, adding "there is nothing illegal or unsavory about this business whatsoever."

Federal officials believe the volume of cash exchanges suggests otherwise. There is no evidence that bank officials were consciously cooperating in money laundering, the officials say. But, says Treasury official Walker, "This pattern of small bills coming in from a tax-haven country is consistent with the same pattern of money laundering that we saw in south Florida."

The Justice Department is continuing to conduct a criminal investigation into the transactions with the Swiss banks. But, "If we would have had those reports from the Bank of Boston when we should have, we would have been alerted to possible money laundering going on from Switzerland to the U.S. years ago," Walker said.

There is no apparent connection between the Swiss transactions and the Bank of Boston's business with the Angiulo family. But that has hardly proved helpful to bank officials. Two real estate companies controlled by the Angiulos, both in Boston's Italian neighborhood in the North End, somehow had been placed on a special bank "exempt" list, which means their cash transactions in excess of $10,000 did not have to be reported to the IRS.

But, according to federal regulations, the exempt list was only supposed to be for retail outlets such as grocery stores that do large amounts of cash business. Nor were the Angiulos exactly unknown in the community. According to a pending federal indictment for murder, extortion and racketeering, Jerry Angiulo has been the "underboss" of a "secret criminal organization" that was "known by various names, including La Cosa Nostra, Stu Cosa, The Mafia, This Thing of Ours and This Thing."

In his most recent press conference, Chairman Brown acknowledged that unspecified bank officials showed "poor judgment" in putting the Angiulo companies on the exempt list. Brown and other bank officials also said they have conducted their own year-long probe and have found no evidence that any employes benefited in any way from the Angiulos.

The Justice Department is doing its own investigation of the Angiulo accounts and the bank's problems with the community are continuing. One Boston suburb has withdrawn its town funds from the Bank of Boston and there have been bills introduced in the state legislature and the city council to do likewise. The bank's downtown office has been bombarded with hundreds of phone calls from its customers, some from indignant depositers who wanted to withdraw their money. Other callers are just worried, says bank spokesman Taylor.

"I took one call from an elderly woman in a nursing home who said she had her life savings on deposit with us and she wanted to know if it was safe," said Taylor last week. I told her that this institution is as financially strong as its ever been. . . . But there's a lot of confusion out there, a lot of people who want to know what the heck is going on."