The stock market took a pounding today, reacting primarily to a sudden new tightening of credit by the Federal Reserve Board on Monday which sent interest rates higher again and apparently caught the market completely by surprise.

As a result, stocks opened lower and kept falling throughout the day. The Dow Jones average of 30 industrials closed the day down 11.44 points at 806.91. In trading on the New York Stock Exchange, declines outnumbered advances by more than 3 to 1. Volume, however, was a relatively light 17.1 million shares, up only slightly from the day before when the Dow industrials slipped 4.33 points.

What particularly upset the market was that the Fed would tighten at a time when the Treasury Department is engbillion-dollar financing operation, a period during which the Fed normally keeps interest rates stable to facilitate the government's borrowing requirements.

Analysts interpreted the Fed's move as an indication that it knew something other investors didn't know, namely that the basic money supply - which the Fed has had great difficulty in controlling - will take another large jump when figures are released after the market's close this Thursday.

"The action of the Fed in the face of the Treasury financing was a shocker," commented John Smith, general partner with Fahnestock & Co. "In my view, the Fed may have gotten a little panicky, and what it did was knock the market on its tail."

On Monday, the Fed's action raised the benchmark federal funds rate from 6.5 per cent to 6.625 per cent, a level that was maintained today.

The market normally recoils in the face of higher interest rates, noted Leon Cooperman, head of the investment policy committee at Goldman, Sachs & Co. "But the recent round of tightening in the face of the administration from the White House last week about what rising interest rates will do to the economic recovery also heightens the speculation about the reappointment of Mr. (Arthur) Burns" as chairman of the Federal Reserve Board, he added.

And if Burns does not get reappointed, the markets will be disappointed "because he's viewed as one of the western world's foremost fighters of inflation," and speculation about his successor will create added uncertainty about the policy outlook, said Cooperman.

Some market analysts said stocks could be in for some pretty rough weather in the days ahead, with the Dow average considered likely to drop below the 800 level again.

"It is going to be absolutely fasten-your-seat-belts time for a while. I'm afraid," said Gary B. Helms, in charge of investment policy for Leob, Rhoades & Co. "When you get into the latter stage of market decline, you tend to get very volatile markets, and I see all of the earmarks of that.We can expect to get some double-digit moves in the averages for a few days."

Helms, who remains fundamentally positive about the stock market, said he was hoping for a "selling climax" to develop and "shake out the weaker hands" in order to allow the market to rebound. "But I think it's going to be scary for a few days."

Besides the Thursday money market report - which will have been largely discounted by the time it is released - analysts anticipate that the wholesale price index for October to be released Friday may show a return to double-digit inflation because of higher farm prices.In addition, capital spending surveys due to be released in the next few days are expected to be less than bouyant in their prospects for business expansion plans in 1978.

The only thing in the news back-ground viewed as somewhat positively today was the call by Charles Schultze, chairman of the Council of Economic adviser, for business tax cuts to stimulate investment.

But even here, analysts pointed out that only a week ago president Carter was shelving plans for tax cuts for stimulating the economy along with any tax reform program for the time being. And they therefore saw Schultze's statement as another example of contradictory policy signals emanating from Washington.

"The statement by Schultze might be greasing the way for Carter to change his tune somewhat," said Smith of Fannestock, but he added, "Carter looks like he's a little confused, to say the least. Meanwhile the market is out there with no support."

Vetco was the most active NYSE stock and was down 3/4-point to $23.125. Combustion Engineering has made a tender offer for Vetco at $23 a share. While Smith International today announced it no longer is trying to seek control of Vetco. AT&Y was off 5/8 to $58.875 among the most actives, and General Motors also dropped 5/8, closing at $66.625.

The broader NYSE common stock index closed the day off 0.52 point at 50.13.

On the American Stock Exchange, prices also tumbled, with the Amex market-value index dropping 1.06 points to 111.96, and the average share losing 9 points.