The much-maligned American dollar soared yesterday against major currencies as traders sought a haven from wildly fluctuating stock- and metal-market prices. The dollar was at its highest against the usually strong German mark since December 1978 and at its best price against the Swiss frac since July 1978.

Gold, traditionally a refuge in times of financial uncertainty, continued its slide, closing down $33.50 in New York at $463, far below its $875-an-ounce peak earlier this year.

And silver prices suffered a major collapse, tumbling all the way to $10.85 an ounce from $16.25 Wednesday, and massively short of an earlier peak of $50 an ounce.

The dollar now has moved 15.1 percent higher against a group of 11 major currencies from its low point in October 1978 that triggered the first dollar rescue package of the Carter administration on Nov. 1 of that year. Five percentage points of the recovery have come in March alone. Economist Edward M. Bernstein noted that the 15.1 percent recovery approached the 20 percent decline in the dollar in the 13 months prior to the rescue package.

Foreigners have tended to regard the combined White House and Federal Reserve anti-inflation package announced March 14 as even more meaningful than have the general evaluations here in the belief that the Fed's credit restrictions will bite hard at the U.S. inflation rate.

Yesterday's upward move of the dollar, continuing the trend of the past two weeks, was especially dramatic because certain psychological barriers were achieved or breached. Among these were the plunge of gold below the $500 level and the rise of the dollar to 1.90 German marks and 1.80 Swiss francs.

These precise points are followed by the chartists among speculative groups. Once having hit the 1.90 level for German marks, the dollar continued to close at 1.9225, up from 1.8915 on Wednesday, the highest close since May 1979. After piercing the theoretical 1.80 barrier in Zurich, the dollar jumped to 1.8330 Swiss francs from 1.7905 Wednesday. The West German central bank made an unsuccessful effort to drive the dollar down, while the Swiss National Bank simply withdrew from the market.

Privately, European currency dealers said they expect more of the same in today's markets. The story was similar yesterday elsewhere in Europe and in Japan, where the dollar rose from 249.10 yen to 249.65 yen.

The basic reason behind the dollar's strength is the spectacular upward move in U.S. interest rates since the announcement of the new U.S. anti-inflation program.

With short-term interest rates running at 17 percent, 18 percent and more, investors have available what amount to record differentials over the yield they can earn in many European countries.

For example, in contrast to yields on U.S. Treasury bills in the 16.5 percent to 17 percent range, the three-month German rate yesterday was 9.65 percent. The 90-day Swiss bank rate was 6.88 percent, while short-term Dutch bank deposits paid 10 5/8 percent. Short-term rates of 14 percent in France and 16 percent in England were closest to the U.S. rate. There were similar, but less pronounce, differentials in favor of U.S. investments in the longer-term bond markets.

European investors, moreover appear to anticipate not only that U.S. interest rates will remain high, but that they will move up even further. "There really is no point in buying gold when investors can get high interest rates on dollars," a Swiss gold dealer said.

Or, as Sam Nakagama put it in an interview with The Washington Post, "Why would anyone want to pay carrying charges of 20 percent on gold when he can get almost that much putting money into dollars?"

Nakagama also suggested that in addition to the interest-rate differentials, financial analysts have come to realize that Europe and Japan would be affected much more seriously by any interruption in Persian Gulf oil supplies than would the United States.

Moreover, the United States physically is farther removed from the scene of any conflict that might develop in the Middle East or south Asia, and traders see this as another reason for securing their money in U.S. investments.