DAMMAM, SAUDI ARABIA, AUG. 30 -- The vast and rich expanse of desert in eastern Saudi Arabia has become the unlikely place where modern pressures building on this ancient kingdom seem to concentrate.

Although oil has been pumped from under the region's sands for half a century, Saudi Arabia's Eastern Province has been faced in recent times with the Iran-Iraq war just offshore, with a Shiite minority that took at least a glance toward Iran's version of Islam and a crash industrialization project that has forced a hasty marriage of Bedouin ways and 20th-century technology.

Among the reminders of the Persian Gulf war that has become an increasing threat to Saudi Arabia, was an AWACS surveillance plane climbing from a base at nearby Dhahran with its radar disc gleaming in the sun and swept-wing fighters streaking through the pink sky over Dammam at dusk.

With most of Saudi oil wealth buried under the sand here and with a giant petrochemical industry under construction at nearby Jubail, Saudi officials have expressed fear that this Eastern Province would be the logical first place for hostilities if Saudi Arabia should become involved in armed conflict.

Prince Mohammed, the provincial governor and a son of King Fahd, said at a meeting with foreign reporters today that because of the Eastern Province's location and wealth, security precautions have been increased in the area's oil fields and refining facilities since hostilities intensified in the gulf.

"Anything that happens, war or anything, this will be the first target," he said.

Mohammed and other Saudi sources have spoken chiefly of their military readiness to meet any Iranian attack, citing the armed forces' buildup over the last two decades. But other observers point to the danger of sabotage or terror raids in a country with miles of unsettled coastline along the gulf.

Mohammed said there have been no incidents of this kind, even in the month that has passed since Saudi and Iranian rulers began trading charges over the killings of hundreds of Saudis and Iranian pilgrims at Mecca on July 31. An explosion and fire at a Saudi gas liquefaction plant Aug. 15 was accidental and injured only four persons, he asserted.

Since the violence, the Saudi royal family has adopted a stiffer attitude toward Ayatollah Ruhollah Khomeini's revolutionary Islamic government across the gulf.

Although the Mecca incident has been Fahd's main concern, his government's toughened policy also has coincided with increased risk of military conflict just offshore from here, where U.S. warships have been escorting reflagged Kuwaiti tankers.

At the same time, Iran has vowed to retaliate against Arab nations for Iraqi air strikes against its oil loading and shipping facilities. These attacks resumed yesterday, after a long lull, and continued today.

Nearby Kuwait, which backs Iraq and serves as a transshipment point for war supplies, has been considered here as the first likely target for any Iranian strikes.

But in their retaliation threats, Iranian rulers also have mentioned Saudi Arabia's multimillion-dollar support for Iraq, and most of the millions are produced in this region.

The Shiite minority here, estimated to number more than 150,000 out of a provincial population of 1.5 million, has been cited as a source of potential unrest or sedition as conflict with Iran has grown.

Riots broke out in this area in late 1979 after the Grand Mosque in Mecca was taken over by radicals denouncing what they said was western corruption in the kingdom.

Mohammed and other Saudi sources said, however, that last month's Mecca violence and Iranian attempts to blame Saudi rulers provoked no disturbances among the area's Shiite population. According to foreign observers, Mohammed, 37, a graduate of the University of California at Santa Barbara, has concentrated on removing discontent and preventing unrest among the Shiites since taking his post 2 1/2 years ago. A number of Shiites jailed following the 1979 protests were released soon after he was appointed in a gesture widely applauded by prominent Saudi Shiites, these observers said.

"We are here to try to make the area as calm as possible," Mohammed declared.

The Saudi royal family has long been part of the austere Wahhabi strain of Sunni Islam, and conservative Moslem tenets have become the law of the land.

But Saudis of the Shiite sect, like their coreligionists in other parts of the Arab world, traditionally have occupied the lower rungs of society.

Mohammed acknowledged that some Saudi Shiites had looked with favor on Khomeini's Islamic revolution when it began in 1979. But he said they since have turned away from Khomeini because of the direction the Tehran government has taken under his leadership.

As a result, Mohammed said, Saudi Shiite religious leaders met with Mohammed soon after the Mecca incident to express indignation at the conduct of Iranian pilgrims.

"Here in the Eastern Province, if perhaps people found a surface attraction at the beginning, when people began to realize what things were like, they changed," he said.

Mohammed has adopted a style of rule that seems anachronistic in a region hurtling ahead with modern economic development.

While construction workers at Jubail hammer on a modern petrochemical complex to process the region's oil, for example, the prince holds a traditional daily majlis, or audience, to receive petitions from his subjects in a style made famous by his Bedouin forefathers.

An elderly Bedouin with a land dispute and a crippled young man who wanted a transfer from his job as a telephone operator were among the petitioners who filed before the seated prince today, handing over written entreaties and arguing their cases in brief conversations.

To an outsider, this princely contact with the people was hard to reconcile with the jutting pipes of Jubail and the ultramodern buildings that Saudi officials said will become a city of up to 280,000 residents, working with some of the world's most advanced technology, by 2010.

But Saudi officials appear to be convinced that they can embrace the West's technology while rejecting its customs.

Bakr Abdullah, rector of King Fahd University of Petroleum and Minerals in Dhahran, said his institution was designed specifically to shepherd this "move of Saudi Arabia from a tribal society and an agricultural society into an industrial society" without abandoning traditional Saudi values.

While Mohammed, dressed in robes and standing beside a paper shredder, spoke to visitors, another educated Saudi official discussed the social benefits of such Moslem laws as the one prescribing amputation of a hand as the punishment for theft.

"We have had a shift in the last 10 years, with all the development, and it didn't change our traditions and customs," Mohammed said.