Stock prices tumbled for the second straight session today, driving the Dow Jones industrial average down 16.81 points to 828.07 it lowest level since the first week of the year.

Oil stocks, the market's strongest group of late, bore the brunt of the selling pressure.

Analysts said the inflation and interest-rate worries that have been battering the bond market for some time appeared to spill over into the stock market.

Meanwhile, bond prices plunged.

Government issues fell 11/32 inintermediate and 1 21/32 in long maturities. Short-term governments declined 20/32, according to the investment banking firm of Solomon Brothers.

Among corporate bonds, industrials fell 2 points and utilities dropped 1 1/2 points. Trading was moderate.

Three-month Treasury bills were up 38 basis points to 15.70 percent, six-month bills jumped 40 basis points to 15.20 percent and one-year bills rose 27 basis points to 14.15 percent.

Dollar bonds fell between 3/4 points and one point in moderate trading. General obligations were down 1/2 point in light activity.

Federal funds -- the loans of uncommitted reserves among Federal Reserve System member banks -- traded at 16 7/8 percent.

And gold and silver plummeted in New York in selling fueled by an easing of tensions over the U.S. hostages held in Tehran. Record interest rates -- and rumors of still higher rates to come -- again buoyed the dollar in overseas trading.

With today's decline, the Dow Jones average of 30 blue chips completed the process of wiping out its gains in the rally of January and early February that took it as high as 903.84 on Feb. 13.

The daily tally on the New York Stock Exchange showed more than eight losers for every stock that gained ground, with 1,491 issues in the minus column and only 175 on the plus side.

Multipoint losers in the oil group included Mobile, down 7 1/8 at 82 3/8; (SECTION) tandard Oil of Indiana, off 6 at 104 7/8; texaco, down 2 3/8 at 37 5/8; and Standary Oil of California, off 2 3/4 at 78 1/4.

On the American Stock Exchange, Bow Valley Industries lost 5 7/8 to 43 7/8, Dome Petroleum 3 7/8 t 65 1/8, McCullouch Oil 1 to 11 7/8 and Houston Oil and Minerals 7/8 to 26.

The oils had been consistently strong of late, even in many periods when the rest of the market was flat or declining.

"This had to happen," said Robert Stovall at Dean Witter Reynolds. 'You can't have one group like the oils standing on a stilt while everything else is sinking."

Even the gold and other metals issues, which had moved up against the market current Wednesday, joined intoday's decline. Homestake Mining was off 2 1/2 at 60 5/8, ASA 1 7/8 at 49 3/8, Dome Mines 4 1/8 to 73 5/8 and Campbell Red Lake 3 1/2 to 35 3/4. In the copper group, Asarco fell 3 3/4 to 51 1/2, Kennecott 3 1/4 to 36 1/8 and Phelps Dodge 2 to 41.

Big Board volume totaled 49.61 million shares against 49.24 million Wednesday. The exchange's composite index slumped 1.44 points to 61.94. Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, came to 50.42 million shares.

Standard & Poor's index of 400 industrials dropped 2.85 points to 123.71, and S&P's 500 stock composite index was down 2.48 points at 108.65.

Analysts said investors seemed to have grown increasingly doubtful that stocks could maintain a steady or upward course in spite of the recent near-collapse of the bond market.

The divergence of the two had reached the point where bond yields exceeded those on stocks by a record spread, presenting stiff competition for investors' funds.

The Amex market value index lost 10.11 points to 286.26 for its biggest drop since it dropped a record 12.26 points last Oct. 9.

In the over-the-counter market, the NASDAQ composite index fell 4.30 points to 148.64.

McCormick & Co. Inc. of Baltimore was the third most active OTC issue on a volume of 254.085 shares at 27 1/2, up 4 3/4. The spice company said Sandoz Ltd. of Switzerland has made a $37-a-share offer to acquire McCormick, and the chairman of Sandoz has been invited to meet with McCormick's board next Wednesday.

Geico Corp., the holding company for a group of D.C.-based insurance companies, with fifth most active on the OTC at 184,000 shares. It closed at of 11 1/8, down 1/4.

In Zurich the price of gold fell to $626.50 an ounce from $644.50 at Wednesday's close. It closed in London at $627.50, down from $646.50, and in New York at $610, down from $636. The price of silver plunged to $33.25 from $36.25 Wednesday.

The Comex settlement price for gold was $607 an ounce compared with $634 Wednesday and down $36 from Tuesday's price. Silver settled at $33.10 an ounce down from $36.05 Wednesday.