The stock market staged its biggest one-day rally in history yesterday, but many Wall Street analysts disputed President Reagan's declaration that the crisis appeared to be over.

The Dow Jones industrial average soared 186.84 points to 2027.85, propelled by investors looking to pick up bargains and the announcement of stock buyback plans by more than 90 corporations.

The surging stock prices on all major U.S. exchanges were part of a global rebound from Monday's historic drops, which wiped out more than $500 billion in domestic stock market value. The continuing huge volume of trading is confronting Wall Street with an unprecedented administrative challenge as firms prepare to deliver securities to buyers.

Securities and Exchange Commission Chairman David S. Ruder said he had directed the agency's staff to undertake an immediate review of the market plunge Monday, when the Dow fell 508 points, to determine what steps should be taken to limit volatility in the future. Much of Monday's drop has been blamed on computer-driven program trading in stocks and stock index futures.

Wall Street executives responded to the calls for reform by suggesting regulations that would limit daily swings in stock index futures prices. They said daily price limits similar to those that exist in other futures markets would help to prevent a repeat of Monday's downward spiral.

After the stock market closed yesterday, President Reagan was asked whether he thought the Wall Street crisis was over. "It would appear to be," the president said. "Certainly when more than half of the loss has already been regained, that sounds as if someone has discovered the economy is still rather sound."

Interest rates continued to decline yesterday, which analysts attributed to a Federal Reserve pledge to provide the economy with any money it may need to continue operating smoothly.

Even though the Dow average of 30 industrial companies posted a strong gain for the second consecutive day, market analysts were not convinced that the market had hit its lows. Instead, several analysts predicted that the stock market rebound was providing temporary relief in advance of a decline that would test Monday's lows.

"I think it is getting a little too optimistic too soon," cautioned Kidder, Peabody analyst Dennis Jarrett. "People are not crying in the streets as a result of Monday's action, which means they are already starting to put it behind them. That is not good in the longer term. We have turned the corner too fast on the psychology."

"In the same way that Monday was definitely an overdone situation, I think this is a snap-back situation that in its own way is overdone on the upside," said Merrill Lynch market analyst Walter Murphy. "It is Monday reversed."

The analogy circulating among traders yesterday was that the stock market resembled a department store that advertised discount prices. The bargain-hunters who grabbed shares included individuals as well as foreign and domestic institutional investors. "Stocks were on sale, but you had to come in and pick up the distressed merchandise quickly," said Bonnie Wachtel, vice president of Washington-based Wachtel & Co. "One of my clients said he looked at the closing prices in the newspaper and it looked like a lot of stocks were just being given away. Many investors who went to buy today were quite surprised at the swiftness and strength of the rebound."

Among the major gainers, CBS Inc. rose 13 to 168 3/4, Teledyne Inc. increased 16 1/2 to 286 1/2 and Vulcan Material jumped 20 to 122.

Among the missing elements in trading activity yesterday was the tremendous volatility that wreaked havoc on the markets earlier this week. The Dow average moved up 105.77 points in the first 30 minutes of trading and continued its rise for two more hours until it was up about 200 points. The gain declined to about 160 points by noon, before staging an afternoon rally that sent the Dow to its record 186.84 gain. Volume was 449.35 million shares, down from the record 610 million traded Tuesday.

At 2027.85, the Dow average has recovered 56 percent of the value lost on Monday. While the average remains 700 points below its high for the year, it is about 120 points higher than the Dec. 31, 1986, closing price of 1895.96.

According to Jim Freeman, a managing director of First Boston Corp., the lack of volatility in the market yesterday was due in large part to the absence of substantial computer-directed program trading.

The New York Stock Exchange had requested that its members not use the exchange's electronic order system to execute programs. The narrowing of spreads between the price of stocks and certain stock index futures contracts also discouraged traders from using computer programs to capitalize on the difference in prices between markets.

On Monday, after stock prices dropped early in the day, traders utilizing a sophisticated asset management technique known as portfolio insurance began selling stock index futures on the Chicago Mercantile Exchange. The sale of the Standard and Poor's stock index futures -- contracts representing a basket of 500 stocks -- by institutions is designed to limit the losses on stock that they own.

But after these heavy sales depressed the price of stock index futures, other traders profited by buying the index futures and simultaneously selling the stocks that comprise the Standard & Poor's 500 index. The sale of stocks by these traders further depressed stock prices, prompting the cycle to repeat.

In effect, it was the decline in stock index futures prices that continually exerted downward pressure on stock prices in a free fall that ended when the market closed for trading.

"We have a situation where we have recreated the Frankenstein monster," First Boston's Freeman said. "It is like having a pill in one hand that you take to solve a problem, having a pill in another hand that you take to solve another problem, but when you take the two pills together it kills you."

Freeman said the stock index futures decline's influence on stock prices Monday was a case of the "tail wagging the dog." He and others on Wall Street said that to prevent another market meltdown in New York caused by futures trading in Chicago, it is necessary to institute daily price limit moves on the index futures.

An official of the Commodity Future Trading Commission said last night that such reforms could either be enacted by the Chicago Mercantile Exchange, with the approval of the CFTC, or ordered by the CFTC.

Other Wall Street sources said the volatility caused by program trading could be limited by increasing the minimum deposit required to buy stock index futures contracts.

Freeman said the broad-based stock market rally yesterday, in which advancing issues outpaced declines by more than 8 to 1 on the NYSE, was driven in part by the announcement of more than 90 stock buyback programs. Companies announcing such plans included Mohasco Corp., which recently moved its headquarters to the Washington area, Greyhound Corp. and others. They followed similar announcements by dozens of corporations on Tuesday.

The companies have said that given the steep drop in stock prices, they believe that repurchase of their own shares is a good use of cash. Wall Street sources said that one of the factors driving the stock buyback programs was a fear that if prices remained depressed, some of the companies could become the target of hostile takeover bids.

One of the companies to announce a stock buyback program was Dayton Hudson Corp., the Minneapolis-based retailer that has been battling a takeover bid from Washington's Haft family. The Hafts withdrew the takeover bid on Tuesday, citing the considerable uncertainty in the stock market. Meanwhile, Dayton Hudson said it planned to buy back up to 15 million of its shares, a move that should help to boost its depressed stock price.

Wall Street sources said the absence of new takeover bids this week, given the low price of many stocks, was due largely to a controversial measure passed last week by the House Ways and Means Committee. The proposal would limit the deductibility of interest on money borrowed to buy companies to $5 million a year.

Wall Street investment banking firms, which have benefited greatly from the spree of deal-making activity that has accompanied the bull market since 1982, are lobbying to ensure that this measure is killed as soon as possible. They told government officials yesterday that a repudiation of the proposal would help to spur a stock market rebound by encouraging takeover bids.

Meanwhile, more casualties were reported in Chicago and New York yesterday, as smaller firms were unable to continue in business due to market losses. However, the firms that failed in New York existed primarily to invest their own capital, rather than public customers' funds.

The NYSE said that it suspended three of its member firms: Wm. D. Mayer & Co., Metropolitan Securities and AIG Inc. Sources in Chicago said at least one firm specializing in futures trading had officially thrown in the towel, with many others expected to close their doors.

Merrill Lynch absorbed one NYSE specialist firm that lacked sufficient capital to continue operating on the exchange floor.

In addition to the record increase in the Dow yesterday, the American Stock Exchange index closed up a record 23.81 points to 281.97, while the over-the-counter market index jumped a record 24.07, to close at 351.86. Heavy volume continued on all major exchanges, including the NYSE where about 450 million shares were traded. On the Amex, all but one of the five stocks that had not traded since last Friday began trading yesterday. One of those, Washington Post Co., closed down 22, at $199 a share.

"There were a lot of value buyers in the marketplace today," said Joseph Hardiman, president of the National Association of Securities Dealers. "We had a significant number of buyers coming in from all over the country and all over the globe. "We are now looking at how to settle and clear all of these transactions we have executed on behalf of customers the last few days."

Hardiman said the settlement problem was one he didn't mind, given the rebound in stock prices. "The markets have a much firmer tone to them," he said.