Stock prices plummeted today as the Dow Jones industrial average closed at its lowest level in nearly two years.

Bond prices, which rallied briefly last week after President Carter announced his newest anti-inflation program, continued the decline that began last Thursday. Long-term government bonds lost about $22.50 off a face value of $1,000.

The Dow average fell 19.71 points to close a 765.44, the lowest for that average of 30 large industrial stocks since April 6, 1978, when it closed at 763.95.

Analysts said stock and bond prices have been dropping because of inflation and because of the impact the separate markets see from the Carter program, announced a week ago Friday.

Because the program wields its biggest stick on the credit and monetary policy fronts, stock traders think the president has guaranteed a deeper recession than might otherwise have occurred. Recessions mean lower corporate profits.

To the bond markets the Carter program means at least a short-run increase in prices and interest rates, developments which are anathema to fixed-income securities such as bonds. Because interests rates don't change on a bond, when interest rates in general rise the price of the bond falls.

"Whether you buy the Carter policy as effective in the long run or not, it becomes clear that in the short run it is not going to do anything good for inflation while it will do a lot of things that are bad, said Robert Peck of Merrill Lynch, Pierce, Fenner & Smith.

The tax on crude oil will push up the price of gasoline, while steps to restrain credit will boost interest rates, two changes that will make the consumer price index worse in the months to come, Peck said.

Last week bond prices lost about $15 on a $1,000 face value -- after a $15 increase early in the week was wiped out by $30 in losses on Thursday and Friday.

Trading in bonds has been light in recent weeks, in large part because of the heavy losses that all bonds -- government, corporate and municipal -- have taken since the first of the year. A bond that was worth $1,000 on Jan. 1 is worth about $800 today.

Since the president announced his program, the Dow average has declined nearly 5.7 percent, from 811.69 on March 14 to 765.44 today. The 19.71-point decline registered today was the biggest since last Monday -- the first day of trading after the Carter announcement -- when the Dow fell 23.04 points.

Stock prices started the day on the decline and, except for a few minor rallies, continued to fall all day. They closed at their lowest level of the trading day.

Only 132 issues on the New York Stock Exchange rose, while 1,527 stocks fell in price.

More than 39.6 million shares changed hands compared with 32.2 million on Friday. The New York Stock Exchange index closed down 1.77 points to 56.47 a 3 percent drop. The New York index is a broader indicator of the movement of stock prices than the Dow index, although the Dow industrial average is the best-known barometer of the market. The Dow average fell 2.5 percent today.

On the American Stock Exchange, the index fell 11.61 points to 241.17.

The list of losers was filled with blue-chip names such as international Business Machines, down 2 3/8 at 54 3/8 and trading at its lowest levels since 1975: American Telephone & Telegraph, off 3/4 at 46 3/8 General Motors, down 1 1/2 at 46 3/4: and Xerox, off 2 1/2 at 53 1/4.

Oil issues also took a pounding. Exxon which cut its U.S. price for heavy fuel oils, fell 1 1/2 to 57 Mobil 3 1/8 to 67 1/2 Gulf Oil 2 to 8 7/8. hTexaco 1 to 33 5/8 and Standard Oil of Indiana 4 1/2 to 96 1/4.

At 4 p.m., General Public Utilities was the most active NYSE-listed issue, off 1 1/4 to 4 in trading that included a block of 250,000 shares at 3 1/2. A major utilities analyst said on the "Wall Street Week" television program Friday that he doesn't think the owner of Three Mile Island could survive in its present setup.

K mart was the second most active NYSE-listed issue, off 1 1/8 to 17 5/8 in trading that included a block of 750,000 shares at 17 3/4.