NEW YORK, NOV. 10 -- Shearson Lehman Bros. Inc. and First Boston Corp. today said they suffered significant losses stemming from the stock market's October collapse, further revealing the extent of the financial damage from the downturn.

Shearson and First Boston also indicated they were studying cost-cutting measures that could involve hiring cutbacks, layoffs or other methods of streamlining.

Shearson, which is 60 percent owned by American Express Co., lost $70 million after taxes in October, largely because of its role in the underwriting of the $12.4 billion offering of stock in British Petroleum Co. PLC.

First Boston indicated that it lost money chiefly from risk arbitrage operations, but declined to specify the dollar amount of its setback. Published reports put the loss at about $60 million based on revenue estimates for First Boston's various lines of business.

Many brokerages and investment houses are thought to have lost money in the Oct. 19 collapse of stock prices, although only a few have made disclosures.

Shearson said about $46 million of its October loss was for an after-tax charge stemming from the British Petroleum underwriting.

The rest of Shearson's loss stemmed from other unspecified stock market activities, a spokesman said.

First Boston disclosed its stock market losses in an internal memo to employes from chief executive Peter T. Buchanan.

Buchanan said First Boston employes "will be hearing a lot more about expense control" but did not indicate that major staffing cutbacks were in the offing. He also stated he did not expect First Boston to leave any product lines.