A federal grand jury has been investigating whether a Washington-based official of Wheelabrator-Frye Inc. received inside information in 1981 that the government of Kuwait was about to buy a California oil company, and used that information to make a profit of more than $500,000 within a few weeks trading the company's stock.

The official, Thomas A. Peacock, director of government relations in Washington for Wheelabrator-Frye Inc., allegedly received inside information on the planned 1981 takeover of Santa Fe International Corp. from an employe of Timmons and Co., a Washington lobbying and public relations firm, according to informed sources. Evidence concerning the alleged insider trading has been presented to the grand jury by the fraud section of the U.S. Attorney's office in Washington, sources said.

William E. Timmons, president of the company and once congressional liaison chief to President Nixon, had no involvement in the alleged incident and has cooperated fully in the investigation, according to the sources.

Timmons' firm was hired to assist in the acquisition.

Michael Reed, general counsel of the Timmons company, said, "We are aware of an investigation. Timmons and Co. has been advised by the Justice Department that we are not a target of the investigation. We have cooperated with the Securities and Exchange Commission and Justice."

Peacock, asked by a reporter about the allegations, said, "I'm not going to talk about it . . .I have no comment."

The grand jury investigation followed an SEC investigation into unusual movements of Santa Fe stock prices prior to the takeover. Under the chairmanship of John S. R. Shad, an appointee of President Reagan, the commission has made insider trading cases a top priority.

As a result of its investigation, the SEC has already brought four separate civil proceedings against people other than Peacock who allegedly had inside knowledge of the planned Santa Fe acquisition. Taken as a whole, the Santa Fe case is considered the largest insider trading investigation in SEC history.

The SEC, which regulates trading in the stock market, has sought criminal sanctions for alleged trading on inside information only five or six times in the past five years, according to Theodore A. Levine, the SEC's associate enforcement chief. He did not comment on whether Peacock was under criminal investigation.

Timmons was informed by Santa Fe of the possible merger on Sept. 28, 1981, according to an affidavit by a Santa Fe official given to the SEC. Timmons warned his employe not to divulge the information, sources said.

The grand jury is investigating whether the Timmons employe told Peacock, an acquaintance, and whether Peacock then purchased Santa Fe stock options, sources said. The options allegedly permitted Peacock to buy the stock at a price well below the figure it eventually sold for, the sources said.

The grand jury is also investigating whether the employe benefitted from the alleged transaction.

At the time Timmons was informed of the merger plan, Santa Fe stock was selling for $22.875 a share. As the takeover attempt proceeded, the price of the stock rose to as much as $30 a share. Eventually, the Kuwait Petroleum Corp. paid $51 a share when it offered to buy the publicly traded Santa Fe in October 1981. The total price paid for the company was $2.5 billion in cash. The takeover was completed in December of the same year.

The prices Peacock allegedly paid could not be learned.

SEC laws and regulations on insider trading are intended to ensure that buyers and sellers have equal access to information that might affect the price of a stock. In practice, many people inside or outside a company must, of necessity, know about events that might affect the price of the stock. For example, lawyers, accountants and investment bankers are usually asked to check out a company before it is acquired.

While federal laws prohibit trading on inside information, it is relatively easy for stock purchases made by an insider to be concealed, securities experts say. In a pending SEC civil court action involving alleged insider trading in Santa Fe stock, the SEC has yet to learn the identities of the purchasers because they used Swiss bank accounts that hide their ownership interest. The Swiss Supreme Court in February turned down a Justice Department request to obtain the identities of the account holders.

Options cost relatively little and give the holder the right to buy or sell stock at a set price over a period of weeks or months. An option costing $2 may permit the purchase of stock at $39. If the price of the stock increases, as an example, to $50, the buyer can acquire the stock for the $39 plus the $2 he or she paid for the option, then sell the stock and make an immediate profit of $9.

Since options are traded just like stock, the trading price of the option will then rise to reflect the increased market price of the stock.

But if the price of the stock remains the same or drops, the buyer may lose the entire investment in the options. Because options magnify the profit that can be made on the spot if a stock goes up in price, they are a favorite vehicle for people with inside information, according to SEC experts.

In one of the more sensational SEC actions involving Santa Fe stock, the commission last year filed a civil case against Gary L. Martin, the Seattle accountant of a Santa Fe director, who allegedly earned $1.1 million on an investment of only $54,000 in Santa Fe stock and options to buy stock. The civil case is pending and Martin has denied any wrongdoing. When commission staff attorneys discovered Martin had transferred some of the alleged proceeds to banks in Tijuana, Mexico, Martin was arrested.

The transfer violated a judge's order and Martin was convicted of contempt of court, receiving a six-months jail sentence, which he said he is appealing.

Santa Fe, now a subsidiary of Kuwait Petroleum, is based in Alhambra, Calif. It drills for oil and performs a variety of oil-related services. It is often confused with another company, Santa Fe Industries Inc., a diversified firm.

The Washington grand jury is also investigating whether Peacock informed his brokers of the takeover plans and whether they acted properly in the alleged transactions.