Many shareholders of Financial General Bankshares Inc. will double their money on their stock if the Washington banking company is sold to Middle Eastern investors.

The biggest profits will be earned by the biggest stockholders -- the officers and directors of the company who, after 2 1/2 years of fighting the sale, agreed last week to drop their objections.

Chairman of the Board B. F. Saul II stands to make as much as $20 million profit on Financial General stock owned by companies he controls, reports filed with the Securities and Exchange Commission show.

Board member Eugene B. Casey of Gaithersburg could come out more than $15 million ahead and Dr. Armand Hammer of Occidental Petroleum, another board member, has a potential profit in excess of $5 million.

The gain for the insiders -- and anyone else who's held Financial General stock since 1977 -- will amount to at least a 100 percent profit in less than three years, if the sale is consumated quickly on the terms now being discussed.

Quick action is unlikely, however, because state and federal banking regulators still must approve the deal. The regulators have yet to face the question of whether the Middle Eastern group ought to be allowed to buy an American bank, because the question has been hung up on legal technicalities raised by the company.

The legal road blocks built by the company's lawyers are the most important reason why Financial General shareholders stand to make so much money if the sale is completed. The opposition has forced the would-be buyers to increase their bid for the bank's stock from the original $15 a share to $20, then $25 and now $28.50.

Further delays will mean a still higher price, because of an escalator clause in the preliminary agreement signed last week by Saul and former senator Stuart Symington, who represents the three Middle Eastern millionaires seeking to buy control of the banking company.

The agreement indicates the takeover of Financial General would have little discernible effect on the thousands of depositors and customers of Financial General's First American Banks in the Washington area.

Control of the holding company has changed hands twice in the past four years without most customers realizing it, and the third shift of power would be inconspicuous if the new investors were not from Saudi Arabia, Abu Dhahbi and Kuwait.

The 12 Financial General banks in the district, Maryland, Virginia, Tennessee and New York will continue to be run by boards of directors from the local communities, with a couple of members of each board chosen by the holding company.

Nor is most of the management of the banks likely change, although Adhams group has already said it plans to bring in a new president to replace J. William Middendorf II.

Saul would also step down as chairman if he accepts Adham's offer but so far he has given no indication that he plans to sell, despite the potential profits. The agreement obligates the company to remove any obstacles that prevent an offer for the stock from being made by the Middle Eastern group, but does not commit the company's management to support the offer actively.

If the sale is completed a year, or even two years, from now, it will radically change the names on the table of organization of Financial General. Washington's third largest bank holding company.

Instead of former Secretary of the Navy Middendorf and real estate investor Saul -- both well-known in Washington -- the principal shareholders of the banking company will become three men until now known only as "the Arabs who are trying to buy Financial General."

Actually, the aren't all Arabs, although their leader, Sheikh Kamal Adham, is a former high government official of Saudi Arabia and is one of the most influential businessmen in the Arab world.

Adham was director of Saudi Arabia's Central Intelligence Agency for many years. He now owns or controls at least nine major corporations, according to reports he has filed with U.S. regulators.

Since 1951, Adham has had the Saudi Arabian franchise for air conditioners made in America by Carrier Corp. For more than 20 years he has operated a 7-Up bottling plant in Jeddah.

Adham's biggest and best known corporation is Al Mabani, a construction company that builds road, airports, sewers and buildings. Other Adham companies import elevators from Switzerland and computers and electronics gear from the United States. He owns a hotel in Saudi Arabia, a beach resort in Lebanon and a travel agency.

The second member of the Middle Eastern group is Abdullah Darwaish, financial adviser to the royal family of Abu Dhabi. Darwaish controls stock bought in the name of Sheikh Mohammed bin Zaid al-Nayhan, a young prince in the royal family that rules the tiny, oil-rich state.

The third member of the group is Faisal Saud al Fulaij, formerly chairman of Kuwait Airlines and an executive of Kuwait International Finance Co., an affiliate of the London-based Bank of Credit and Commerce International, which is widely believed to be owned by the royal families of several Middle Eastern countries.

Former White House budget director Bert Lance has represented BCCI recently and it was Lance who first suggest Adham and his associates attempt to buy control of Financial General.

In the fall of 1977 the three wealthy investors bought about 19 percent of the company's shares in a series of privately negotiated transactions with major shareholders. Paying around $14 a share for their stock, they invested $16 million in Financial General.

The $28.50 a share the three have agreed to offer for the remaining stock amounts to 158.333 percent of the book value of the stock as of Dec. 31. s

If the book value increases before the offer is made, shareholders will still get 158 percent of that value. At the current growth rate, the book value probably will be close to $20 a share by the time the offer can be made, requiring Adham to pay more than $31 a share.

At $28.50, the Middle Eastern buyers will have to spend $147 million to acquire the 5.2 million shares they don't already own; at $31, it will cost them $161 million.

The preliminary agreement also requires Adham, al Fulaij and Darwaish to buy the 564,000 shares of Financial General's Class a Stock, which sells for about 20 percent less than the common stock.

More than a quarter of the Class A shares are owned by board member Casey. At $22.80 -- 20 percent less than $28.50 -- Casey's Class A shares would be worth $3.6 million. Casey also owns about 600,000 shares of common stock, worth another $17 million at $28.50.

Casey has owned some of his Financial General stock since the 1930s -- when it sold for less than $1 a share. If Casey gets $20 million for his stock, he will probably make $15 million profit, sources familiar with his holdings estimate.

Board Chairman Saul's personal holdings of Financial General stock are smaller than Casey's, but through corporations he controls, Saul has almost a million shares, worth $28 to $31 million, depending on the price finally paid.

Saul has not owned his stock as long as Casey, reports to the SEC show, and has paid an average of around $14 for his shares. Saul his pyramided his original investment by reinvesting the cash dividends he has earned on his investment in the past year.

Like other Financial General shareholders, Saul also has benefited from two 5 percent stock dividends that Financial General has paid in the past two years.

The stock dividends amount to a 10 percent bonus for shareholders, and in Saul's case pushes his potential gain toward $20 million.

Hammer, the third largest stockholder, ownes 342,000 shares. He too paid less than $14 a share (under $5 million) for stock that will be worth that much in a $28.50 buyout.

Because the stock is currently selling for about $23 a share, speculators still could theoretically make a profit by purchasing the stock now and waiting for Adham's $28.50 offer.

The interest cost of holding the stock for a year or two would be less than the difference between the current price and the offer, and the escalator clause in the contract adds to the upside potential, analysts point out.

But if regulatory roadblocks prevent Adham from making his offer, the price is sure to fall, probably back to the $14-a-share range where it was trading before the takeover appeared likely.