Amid extraordinary security measures, Nancy Reagan heads off Friday for Malaysia and Thailand, her first solo venture into Third World countries to emphasize her concern about drug abuse.

Mrs. Reagan's trip, coming in the aftermath of a surge of terrorist activities, has taken on another important meaning for the White House: to demonstrate that life must go on.

Conceived and planned under different circumstances, the first lady's journey has come to symbolize the president's determination that normal activities should continue because suspending them would mean victory for terrorists.

Mrs. Reagan's trip, however, will be carried out under far from normal conditions.

Her Secret Service detail has been doubled. The White House has flown its own automobiles into both Bangkok and Kuala Lumpur for her motorcades, turning down offers of cars from the host countries and ruling out U.S. Embassy vehicles. U.S. frogmen almost certainly will be swimming along her route when she takes a boat ride in Bangkok.

Even her own staff is getting precise information about her schedule only on a "need-to-know" basis.

Administration spokesmen will not talk even about what might seem routine aspects of the measures being taken to ensure Mrs. Reagan's safety, which one White House official described as "the highest level" of security.

"But basically, we are confident that we are in complete control and we feel she will be very well protected," he said. He said that U.S. intelligence has turned up no evidence that would reverse the White House decision to proceed with the solo trip.

Aides to Mrs. Reagan denied that she is nervous about the trip, saying she is "no more nervous about this trip than any trip" she takes.

"I think she relies solely on the fact that if security had some intelligence that would mean changing her plans, they would tell her," said her press secretary, Elaine Crispen. "You can't dwell upon it, so we're in a 'go' frame of mind."

But others around the first lady, who is a self-admitted worrier anyway, said she has been unusually tense lately, an indication of her heightened concerns about her mission as well as the safety of her husband and her family.

Reagan, who is said to tend to be somewhat fatalistic about facing danger himself, is very much the concerned husband when Nancy Reagan is involved. "I worry when she goes around the block," he said last week.

Given recent incidents in other countries, part of that anxiety could stem from the fact that Libya has diplomatic missions in both Malaysia and Thailand.

Thailand's vote last week in the U.N. Security Council condemning the U.S. air raid on Tripoli took American officials by surprise and has added another element of contention in relations between the two countries.

The Thais were already unhappy over the 1985 U.S. farm bill, which specifically singles out subsidized Thai rice as a problem and urges selling U.S. rice abroad at less than domestic prices as a way of combating foreign sales.

The subject is one the Reagan administration would prefer to avoid on this trip. But even though Mrs. Reagan is not expected to bring up the rice dispute in her talks with her Thai hosts, it is an uncertain diplomatic and political factor that could be brought up by them.

In Kuala Lumpur, the youth wing of the Islamic Party of Malaysia, a group that opposes the current Malaysian administration, has announced plans to demonstrate, renewing its protest of the U.S. raid on Tripoli as well as of Reagan's warning that similar action might be taken against Iran and Syria, if necessary.

Malaysian Embassy officials in Washington last week downplayed similar protests outside the American Embassy in Kuala Lumpur as demonstrators' means of "only showing solidarity with their Islamic brothers."

Denying that there is any high-level nervousness surrounding Mrs. Reagan's visit, the Malaysian officials dismissed the possibility of terrorist activities, saying, "We don't think the Libyan government would want to embarrass us."

Mrs. Reagan's solo schedule begins Thursday in Bali with a visit to a Balinese "village," which was specially created by bringing in native craftsmen and dancers, and an afternoon tea with Siti Hartinah Suharto, wife of the Indonesian president.

Friday morning the first lady will fly to Kuala Lumpur while President Reagan flies to Tokyo for the seven-nation Economic Summit. The Reagans will not meet again until Monday, when Mrs. Reagan joins him in Japan.

Mrs. Reagan's side trips to Malaysia and Thailand grew out of her desire to take an international aproach to the growing problem of illegal drug use.

After Mrs. Reagan's First Ladies Conference on Drug Abuse at the White House last year, Malaysia's Dr. Siti Hasmah, wife of the prime minister, launched a nationwide parents' movement based on drug abuse prevention through education. Mrs. Reagan will be briefed on the program, meeting with parents and young people involved.

Malaysia is a country through which opium coming out of the Golden Triangle is transported, rather than a producing country, and its addict population has been skyrocketing in recent years. There are an estimated 250,000 users and addicts, approximately 2 percent of Malaysia's population. Of that number, about 70 percent are under the age of 30.

In Thailand, Mrs. Reagan will see a drug abuse exhibit and be given an award for her drug abuse work. Her visit is seen by administration officials as a means of underscoring U.S. appreciation of Thai efforts to curb the flow of illegal drugs.

"We have always emphasized in our relations with Thailand -- and Congress has played a role in that -- that we expect progress in order for there to be good relations between the two countries," said one State Department official.

"We've said it's the highest levels in the U.S. government who are interested in curbing the drug flow, and in that sense, Mrs. Reagan's visit there will make that real," he said.

Current Drug Enforcement Administration estimates are that about 18 percent of the heroin consumed in the United States originates in the Golden Triangle -- an area encompassing parts of Thailand, Burma and Laos -- and exits through Thailand.

Heroin abuse is of growing concern to the Thai government, partly because it is increasing in Bangkok, a spinoff from the regular international trade. Of Bangkok's 7 million population, 200,000 to 300,000 are estimated to be drug abusers.

Jack L. Courtemanche, Mrs. Reagan's chief of staff, said Thailand's king and queen have invited Mrs. Reagan to visit "and while we are there, the queen wants Mrs. Reagan to help get a drug abuse program started."

Yet another reason Mrs. Reagan is going to Thailand is to help make up for the visit Reagan canceled in 1983. The Thais, like the Indonesians, do not consider the current visits substitutes for those Reagan scrubbed in the aftermath of Benigno Aquino's assassination in the Philippines.