Sheik Kamal Adham, the brother-in-law of the late King Faisal of Saudi Arabia, plans to run a rival slate of candidates for the board of directors of Financial General Bankshares Inc., in a new attempt to gain control of Washington's third largest banking company.

Adham already owns about 10 percent of Financial General and heads a group of Middle Eastern investors who have tried nearly two years to buy control of the company, owner of a dozen banks.

The Middle Eastern group has offered to pay $25 a share for Financial General stock that now sells for between $17 and $18 a share.

So far that offer has been blocked by a series of legal maneuvers by Financial General's top management. The bank's chairman is B. F. Saul II, the Washington real estate man; its president is G. William Middendorf, the former secretary of the Navy.

To remove that roadblock, Adham plans to try to oust the company's management by waging what is known as a proxy fight. At Financial General's annual shareholders meeting next April, Adhma will ask shareholders to vote out the old officers and elect new ones nominated by him.

Adham's plans were disclosed in a report to the Securities and Exchange Commission that was made public Saturday by attorney Robert Altman.

The SEC has been monitoring the Financial General takeover fight since January 1978, when the Middle Eastern group secretly bought about 20 percent of the company's stock.

Originally the group was represented by former budget director Bert Lance. Lance dropped out of the deal more than a year ago and lately all actions have been announced by Altman, a law partner of Clark Clilfford.

Besides Adham, who formerly headed Saudi Arabia's central intelligence agency, the group includes Abdullah Darwaish, financial adviser to the royal family of Abu Dhabi, and Faisal Saud al-Falaij, former chairman of the government-owned Kuwait Airlines.

Darwaish and al-Fulaig each control about 5 percent of Financial General's shares and will vote their stock for Adham's nominees to the board of directors, the report to the SEC said.

Because most corporate shareholders don't bother to vote at annual meetings, the election of officers is rarely used as a means of getting control of a firm. But the Middle Eastern group says it intends to try.

Just as in a public election where a powerful office is at stake, hundreds of thousands of dollars can be spent on a campaign to elect new company officers.

The big difference between public and corporate elections is that in business buying votes is not only legal, it is necessary because the more stock you own, the more votes you get.

Financial General has about 6 million shares of common stock, each entitled to 10 votes at the annual meeting and just over half a million shares of Class A stock, worth one vote each.

Public records show that Financial General's present management and the insurgent group each own about the same number of shares.

As of this year's annual meeting, the Adham group owned 18.6 percent of the common stock and Saul controlled 17.8 percent.

The other major shareholders are Gaithersburg investor Eugene B. Casey, who owns about 9 percent of the common stock and 25 percent of the Class A and Armand Hammer, chairman of the board of Occidental Petroleum Corp., who owns 5.2 percent.