In a high, narrow valley of the Andes Mountains near here, the fortunes of Exxon Corp. in military-ruled Chile are starting to turn decidedly sour.

Five years ago, lured by the attractive incentives of the authoritarian government, the U.S. oil conglomerate sank $112 million into the purchase of two medium-sized copper mines and announced a $1.2 billion expansion project that was proclaimed a model of Chilean development.

Now, not much is heard here about that landmark foreign investment in Gen. Augusto Pinochet's "new" Chile. In fact, Exxon -- plagued by technical, financial and bureaucratic problems -- is quietly suspending the project. Having spent $500 million in the mountains, it expects to lose $90 million this year alone.

Exxon's gloomy record is one that has come to haunt the Pinochet government, for Exxon's experience is just one case in what has become an increasingly unsuccessful history of U.S. private investment in Chile's free-market economy.

Although the nine-year-old military administration made foreign investment a foundation of its plan to reorganize and modernize the country, it failed to attract either the capital or the new technology it sought, government officials here conceded.

Meanwhile, as Chile's economic boom of the late 1970s has collapsed in the past 18 months, multinational corporations that were encouraged to open or expand operations after the overthrow of Socialist president Salvador Allende have suffered.

South of Santiago in Concepcion, for example, Dow Chemical Corp. plans to shut its $32 million petrochemicals plant this month for the rest of the year while sustaining a $1 million loss. Firestone's tire factory in Coquimbo, 270 miles north of Santiago, also shut, and the company's subsidiary declared bankruptcy in the face of $22.5 million in outstanding debts.

General Motors is hanging on to its $4 million assembly plant in the northern border town of Arica, despite the closing of two of the three other foreign auto plants in Chile. But, company executive David Herman said, "we know we will have to close down. The government has decreed the death of the automotive industry in Chile."

Closings and losses are in part attributable to the world recession, which has hurt mining investors in particular with slumping prices for ore. But many foreign company executives have joined the Chilean opposition in blaming the Pinochet government for much of the trouble, despite its pro-investment laws.

Many Chilean analysts also charge that the lack of major foreign investment in recent years is in part the fault of the government's very incentives, which are said to frighten off investors -- believing that they will be reversed as soon as the right-wing generals leave office.

While government officials dispute such criticisms, most analysts agree that the lack of major investments poses a real threat to the free-market, monetarist economic program launched by the military seven years ago.

Hoping to reverse decades of pervasive government management of industry, Pinochet's ministers have cut spending, sold state companies and encouraged a flood of imports with the lowest tariffs in Latin America. Large foreign investments are needed to finance the restructuring.

Until now, Chile made up for the lack of foreign investment with foreign loans. But with its foreign debt at $17 billion, which Chilean economists say is the highest per capita in the world, the country cannot afford to borrow much more.

"We are awaking from a dream where foreign capital wasn't missed because we had all the imports and loans," said Juan E. Herrera, a Chilean bank economist. "Now if we do not get foreign investment, it could cause real problems."

For some economists, Chile's experience is a demonstration that favorable government measures alone cannot attract multinational companies to a developing country. Throughout his rule, Pinochet has backed laws governing foreign investment that have abandoned almost all of the traditional controls placed on such capital by other developing nations.

The most dramatic change came in 1976, when Chile withdrew from the six-nation Andean Pact common market to avoid its guidelines on foreign investors. These rules sought to correct past abuses by controlling such practices as the remittance of profits from foreign subsidiaries to home companies and the billing of subsidiaries by multinationals for equipment and other services.

Chile, in contrast, offered contracts to foreign companies that substantially reduced previous tax rates. In the key area of copper mining, taxes went from the 60 to 70 percent range of the late 1960s to 49 percent. Exxon, like other firms, also won an accelerated depreciation tax clause that one private economist estimated would save it from paying any taxes for 10 years.

Some U.S. companies that had bitterly opposed the democratic Allende government -- which nationalized without compensation the major copper mines and intervened in other foreign businesses -- were quick to respond. General Motors, which locked up its Arica plant and left Allende's Chile in 1971, reopened in 1974.

Dow Chemical, which had a government intervenor, was given back control by the military. It spent $2 million on expansions in 1976 and 1978. Firestone paid $7.35 million for 70 percent ownership of its tire plant in 1975 with the government as a partner.

But new foreign investors came slowly in all but the banking sector, where the new free-market policies and foreign loans created a small boom. Between 1974 and 1980, the amount of actual foreign investment only reached 70 percent of the average annual rate of the mid-1960s, when Chile had a Christian Democratic government, according to a study by economists at the Santiago-based U.N. Economic Commission on Latin America (ECLA).

Currently, government figures show that a total of $6.7 billion in foreign investments has been authorized since 1974, but only 24 percent actually has been invested. Moreover, a 1978 government study showed that only 5 percent of the new capital represented transfers of new technology into Chile, as opposed to a rate estimated at near 50 percent in the 1960s by ECLA economists.

U.S. businessmen, who control nearly 80 percent of the foreign capital in Chile, say that much of the industrial investment gap has been caused by the other characteristics of the very economic model meant to encourage it. Most of all, they blame the government's low tariffs on imports and its maintenance of the Chilean peso at a fixed, increasingly overvalued rate for three years, making imports even cheaper and investments in the country far more expensive.

"Why invest in a country when it becomes cheaper just to export to it?" asked an analyst. "What's happened is that the firms already here are losing and the new investments in the productive sector have never happened."

Some of the U.S. industrial firms now in the country, despite success in 1979 and 1980 during a consumer boom in Chile, now say they will not survive unless the government's strict policies are changed greatly, particularly on tariffs.

The most serious investment problems, though, are in the mining sector, the heart of Chile's economy and the focus of more than 80 percent of the authorized foreign investment since 1974. Government figures show that 32 projects had been authorized for $5.4 billion by the end of 1981, and that only 11 percent of these funds -- or $633 million -- had been spent.

Government officials say the slow pace of investment reflects the normally lengthy development of a mine, including long periods of preliminary study, and the low price of copper through much of the period. But other analysts note that the Chilean experience has had other elements.

The largest projected investor, for example, is Anaconda copper at $1.5 billion. But Anaconda's project has been postponed already by three years, according to diplomatic reports, and company officials say they will not now decide whether to go ahead with it until 1984.

Of all the large investments, only two are actually producing minerals after nine years of government efforts, and the first major investor, the Canadian company Noranda, abandoned its $400 million copper mining project in 1980.

Of all the mining investment money actually spent, more than 60 percent has come from Exxon, whose ill-fated La Disputada project has faced poor conditions, difficult planning and bureaucratic tangles since it was launched in 1977.

Presented by the government as proof of its acceptance by big multinational investors, the Exxon project envisioned the expansion of one of its two medium-sized mines, the Los Bronces site in the Andes east of Santiago, into a giant mining operation that would produce 250,000 tons of fine copper annually and transport ore through a 19-mile long tunnel cut through the mountains.

Much of the company's money -- $100 million according to Exxon officials -- has gone into simply studying the project. Exxon spent three years drilling 121,000 test holes to survey its ore body.

There has been bad luck, too: a 1978 avalanche destroyed the already operating pits at Los Bronces and it took 13 months and $7 million to get the operation going again, company officials say.

But Mathew J. Quilter, the deputy Exxon manager in Chile, said that part of the problem has been difficulties with the government bureacracy. While overall relations have been satisfactory, lengthy government delays in the granting of essential permits have been "unhelpful," he said.

Quilter said the expansion project, whose estimated cost has zoomed to $3 billion since 1977, would be unlikely to turn a profit now. He said that while Exxon officials are studying the issue, "the preliminary indication has been not to go ahead." Exxon Mining Co. President William M. McCardell already has been quoted as saying the project will be suspended.

Meanwhile, Quilter said the current mines have faced $160 million in losses in the past two years, including a projected loss of $90 million in 1982. "Exxon is a patient company," he added. "Sometime it will all have to come together and we'll make some money."

Other analysts said, however, that Exxon's troubles in developing the investment may have made other investors think twice about mining in Chile. And although officials from mining companies deny it, a wide range of Chilean and foreign analysts added another reason for reluctance -- the investment law itself.

"It's too good to be true, and the companies know it," said Radomiro Tomic, a former presidential candidate of the Christian Democratic party. "They know that as soon as Chile has a democratic government, these laws will be changed, and they don't know where they will end up."