The master builders of the Bechtel Group have drilled subways beneath San Francisco Bay and the Potomac River, spun pipelines across the Andes and the Arabian desert, and helped prepare Los Angeles for the Olympics.

Bechtel built the Hoover Dam. It is turning a small Arabian Gulf seaport into a city of 250,000 and cleaning up the radioactive mess at Three Mile Island. Its $13 billion in new contracts last year made Bechtel the biggest construction contractor in the world.

That is the past.

Looking ahead, Bechtel is facing a competitive world as intimidating as the rain forests and deserts it tamed to build its projects.The overvalued dollar has pushed up Bechtel's costs painfully, eroding the company's formidable advantages in engineering technology and experience. Bechtel, which relies on its U.S.-based engineers for the bulk of its design work, recently shifted some work to its engineers in Taiwan because costs there are so much cheaper. "Our engineering is now not competitive in many situations," said Alden Yates, Bechtel's president.The downward slide in commodity and energy prices has reduced demand for the huge oil, gas and minerals projects that are Bechtel's specialty, particularly in the Mideast, where Bechtel's close relationship with Saudi Arabia led to billions of dollars in massive projects. Asia has become the most promising arena for major projects, led by China, whose vast resources and industrial development plans make it the new focal point for international contractors.

But to get that business, Bechtel and other American firms must beat out rivals from Europe, Japan and South Korea whose bids are aided by subsidized government credits at a level that the U.S. Export-Import Bank will not match, except in a few cases. Only 5 percent of U.S.-manufactured exports are supported by Ex-Im financing, compared with about 40 percent for France and Japan, and the administration's policy is to try to reduce the use of subsidies in international competition rather than to add to the problem.To win major new contracts, Bechtel and other construction giants have been obliged to act like financiers, arranging billions of dollars in credits for government-sponsored projects that otherwise would not be built. Bechtel has considered barter deals to reduce financing demands, including taking wheat from Turkey as partial payment on a project. And its construction companies have had to arrange complex insurance coverage and currency futures transactions to cover the increased financial risks they face because of their direct involvement in financing.

"The big projects are in the developing world, and they're the ones that have the debt problems. Unless you can find money, you don't get work," Yates said.

But borrowing costs in this country are too high to compete with heavily subsidized foreign credit, and this has forced Bechtel to get financing abroad on some major projects. Japanese credit is financing a major Bechtel venture in New Zealand, and that means a larger percentage of material and services for the venture will come from Japan rather than Bechtel's U.S. suppliers.

For all this, Bechtel remains the largest engineering and construction firm in the world, with $14 billion in revenue from existing projects in 1983, according to Engineering News Record's annual survey of the industry. The company, run by Stephen D. Bechtel Jr., grandson of the founder, Warren Bechtel, is privately owned and does not discuss its profits. However, The Wall Street Journal reported that it obtained company records showing that Bechtel's net worth rose by $128 million last year to $760 million.

Its prestige remains high, buttressed by the presence of two of its former executives in President Reagan's Cabinet -- Secretary of State George P. Shultz, who was Yates' predecessor as Bechtel's president, and Defense Secretary Caspar W. Weinberger, the company's former chief legal counsel.

But 1984 will mark the fourth year in a row in which the value of the new contracts Bechtel booked will be less than the revenue from existing work, an uncomfortable erosion of the company's financial base. Revenue from existing work is expected to fall below $10 billion this year, one-third less than in 1983.

Its nuclear power plant construction business -- an important revenue source until recently -- has withered. Bechtel had to lay off or reassign 3,500 employes this year when Consumers Power Co. canceled its Midland, Mich., nuclear plant project. With that action and other cutbacks, Bechtel's worldwide work force will fall to less than 31,000 from 44,000 two years ago.

Whereas Bechtel and other U.S. firms had 45 percent of the international construction market in 1980, the U.S. share is now down to one-third, said Cordell Hull, Bechtel's chief financial officer.

"Foreign competition is getting much more intense," Yates said in an interview. "Part of this is a natural progression," he added. The commanding lead that U.S. firms enjoyed at the outset of the postwar period could not last.

"Ten or 12 years ago, there was no Japanese firm that had any credibility in designing and constructing a major oil refinery. Now there are several," Yates said. And many others want to join the club of contractors qualified to build megaprojects, a club now limited to U.S., European and Japanese firms, according to Yates. Wherever it does business in Asia and other parts of the developing world, Bechtel is pressed to share its technology and know-how with its less-experienced rivals as part of the price of doing business in their countries.

Some developing countries such as Taiwan, South Korea and Brazil have developed engineering skills to handle all but the largest petrochemical and high-technology projects.

For Bechtel, China represents a new window for megaprojects and the same close alliance with national leaders that it has enjoyed in Saudi Arabia.

"The great opportunity is China," Yates said. "It's five or 10 years away . . . but we're talking about billions of dollars in dams, refineries, coal mines."

Bechtel has formed a joint venture with China's Ministry of Coal Industries, called China-America International Engineering Inc., to help develop China's impressive, largely untapped coal reserves. The prospects make Bechtel's mouth water. Richard Godwin, president of one of Bechtel's three main construction companies, said the Zhungeer mine in Inner Mongolia it hopes to develop has 30-foot-thick seams of low-ash, low-sulphur coal. "I don't think they know how far it goes," Godwin said. "In 15 or 20 years, China could dominate the coal market."

But before that happens, the quintessential capitalists of Bechtel and the communist central planners of the Coal Ministry must cement a relationship. "We're groping, trying to find ways of providing them with our technology, providing them with an understanding of the way we do things," Godwin said.

Bechtel's way of doing things includes a broad delegation of authority to onsite managers, policies on resolving legal disputes and liability when things go wrong, and practices for counting the hourly cost of engineers and other professionals -- none of which is part of Chinese practice at this point, Godwin said. In the process, both sides are steering clear of politics. "I think they keep their rigid people away from us, and we don't try to make them into good capitalists," he said.

But the Chinese are capitalistic enough to drive a hard bargain on project financing.

Yates has been told that to do business in China, Bechtel must find the money to finance the projects at an interest cost of less than 7 1/2 percent a year, because that is what competitors such as the Japanese, Belgians and French are offering, a rock-bottom rate that is possible because of government-subsidized credit.

Hull said he hopes that the U.S. government will provide a total of $2 billion to support American exports to China, but no commitment has been made.

If it chose to, the Ex-Im Bank could compete with foreign subsidies, and it has done so recently in a few instances. To help Cincinnati Milacron land a contract to supply computer-operated machine tools to Indonesia, the Ex-Im Bank provided $15.25 million in financing at a yearly interest rate of 6.5 percent, with a 13-year grace period when no repayment is required, and a 20-year payment term thereafter.

But that is a heavy, costly subsidy that the Ex-Im Bank isn't anxious to repeat, an official said. It borrows from the Treasury at about 12 1/2 percent interest and generally lends at between 10.7 and 13.6 percent. The earnings on its loans, thus far, have made it unnecessary to ask Congress for an appropriation to balance its accounts.

Bechtel's competitors reach very low rates by mixing subsidized loans with grants, so-called "mixed credits." To help U.S. firms compete, Congress has directed the Ex-Im Bank and the Agency for International Development to combine loans and grants in the same fashion, but it hasn't happened.

"AID isn't set up to support exports. It has a different mandate," said Hull -- a mandate to support economic development abroad.

If the U.S. government is unable to curb the use of export credits, it will have to step up Ex-Im Bank lending, or see Bechtel and other U.S. multinationals pay the price, Hull said.

(Another of the high-placed government alumni recruited by Bech- tel is John L. Moore Jr., former head of the Ex-Im Bank, who is an executive vice president of Bechtel's financing group.)

"It's unrealistic to expect that a gentleman's agreement will be able to temper this," Hull said. "The whole world is in a slow-growth environment. . . . Unemployment is high."

And countries will do what they have to do to compete, he said.

"Look at Japan, whose very life depends on exporting. "We have to be put on the same basis as others, or there's no way we can compete against them. But it's an extremely difficult problem. We're facing huge budget deficits, and when the Office of Management and Budget looks at this, they're not going to be very responsive," Hull said.