Equitable General Corp. of McLean yesterday announced an agreement in principle to merge with Great Southern Corp. of Wilmington, a $805-million diversified financial company.

The agreement provides for Great Southern to acquire 1.2 million shares of Equitable General, more than 40 percent of the $2.8 million shares that are outstanding.

For each share of Equitable General, Great Southern will pay $40 cash or one shares of a convertible, voting preferred stock paying a $3 annual dividend. In overthe-counter trading Equitable General shares closed yesterday at $29.50 bid, $30.5 asked.

The merger, announced by the two firms late yesterday, still requires approval of the board of Great Southern and the stockholders of both companies as well as federal and state regulators.

Great Southern is identified by Fortune magazine as the 50th largest diversified financial corporation in the nation. It owes Great Southern Life Insurance Corp. of Houston, a savings and loan association that operates in Utah and Hawaii, an insurance agency, an investment firm, three real estate development companies and other operations.

Equitable General is a holding company whose principal operation is Equitable Life Insurance Company, a direct marketing company with 1.4 million life insurance policies in force.

Yesterday's announcement said Equitable Life would continue to operate with its present management and employes if the two holding companies merge.

Equitable General had been courted by previous merger partners, and rumors of a $40 per share takeover had been prevalent for several weeks.

Equitable General Chairman Charles Phillips could not be reached for comment on the merger plans.

Phillips has been under intense criticism from dissident shareholders who have complained about rejection of previous merger approaches. They also have faulted the company's management for failing to make a acquisitions that were permitted after the company reorganized as a holding company in 1974.

In a lawsuit in Fairfax County, three major shareholders recently accused Phillips and Equitable General's board of directors of acting illegally and imprudently in buying about 500,000 shares of the company's stock.

The shares had been held by American General Insurance Corp., another Texas company, and were bought back by the company last year for $32.50 a share. Phillips defended the purchase as necessary to fend off an unfriendly take-over attempt by American General.

Trading in Equitable General shares was suspended yesterday after the company said an announcement was expected. The stock, which traded in the $26 range earlier this year, had moved up recently.

Under terms of the merger announced yesterday, shareholders will have the option of $40 cash or one share of Great Southern preferred immediately convertible into one share of Great Southern common, which closed yesterday at $27.25 bid, $27.75 asked.

Great Southern has the option to begin redemption of the convertible preferred issue starting in 1986 and is obligated to begin redemption by 1991. The redemption price is $40.

The merger agreement is contingent upon a ruling by the Internal Revenue Service that the exchange is tax-free to Equitable General and also requires a favorable opinion by an independent investment banking firm, which was not named in yesterday's announcement.

The merger announcement came less than a week after critics of Equitable General management sued Phillips and the board of directors. The lawsuit demands the defendants pay back the company nearly $2.9 million that allegedly was misspent purchasing the company's stock.

The lawsuit was filed by the Curtiss Steuart, chairman of Steuart Investment Co., Marshall Garrett, son of a former general counsel of Equitable General, and Andrew Altman, another former Equitable General attorney. Together they own some 300,000 shares of the company's stock and would stand to gain some $3 million more than the market value of the shares under yesterday's merger plan.

The three investors who filed the suit said they contemplated a proxy fight to oust Phillips, but decided it could not succeed. Phillips owns $454,000 shares of the company's stock and is said to control more than half the shares, virtually assuring stockholder approval of the merger.

Phillips, who is 75, has run Equitable General for more than 40 years.