Construction of a new beach motel and bungalows to be run by the Marriott Corp. and a small international airport to receive tourists is being rushed to a finish here as Egypt speeds up its many plans for the development of the Sinai Peninsula.

The resort, situated amid towering palm trees on a stretch of gorgeous sand said to be the nicest in the eastern Mediterranean, is expected to bring a new influx of Israeli, Egyptian and European visitors to this ancient caravan trading center.

For the past three years, El Arish has been best known as the site of the main border post between Israel and Egypt, a crossing that could take up to five hours. But with the withdrawal of Israel, this run-down city of 80,000 will resume its old status as the principal city and capital of all Sinai.

The new resort here, the purchase for $143 million of three Israeli-built tourist complexes along the Gulf of Aqaba and the renowned 6th century Monastery of St. Catherine at the foot of Mount Sinai already seem to have established tourism as the main new vocation of this sparsely inhabited and beautifully sculptured land of giant sand dunes and craggy mountains.

Tourism is not the only activity Egypt has planned for the peninsula. But aside from a few scattered industrial, mining and land-reclamation projects, it appears destined to be the first one implemented pending the completion by the end of the year of yet another master plan for overall development of the Sinai--this one being drawn up by an American consulting firm.

The problem of what to do with this wilderness of rock, sand and palm trees has haunted Egyptian authorities since the hope of getting it back first dawned after the 1973 war. The failure to settle it--there are only 180,000 people in its 23,442 square miles--and the general neglect through years, even centuries, of Egyptian history now are regarded widely in Cairo as a major strategic error.

If there had been people, towns, industries and developed real estate in general, the theory now goes, Israel would not have crossed the Sinai with such speed in the 1967 war.

So Egyptian leaders, planners and economists have been dreaming up plans for years to populate the Sinai and make it bloom.

The late president Anwar Sadat, for example, promised in May 1979 that "greenery will cover the entire Sinai Peninsula and the whole region will be a land of love, peace and coexistence."

Government planners talked of piping fresh water from the Nile River under the Suez Canal and into the desert to irrigate 800,000 acres of land and make the peninsula home for about 2 million of the 44 million Egyptians packed into the narrow Nile Valley.

There have long been plans, too, to exploit the estimated 35 million tons of Sinai coal deposits, partly to provide fuel for a 1,200-megawatt power station to be built in El Arish at a cost of $650 million.

But if Egyptian authorities in the Sinai have learned anything in three years of administering recovered land here, it is that grandiose dreams in Cairo have to be reshaped to fit the national budget and capabilities.

Signs of a new realism were apparent in an interview here with the governor of northern Sinai, Youssef Abu Taleb, a former artillery officer who trained at Ft. Sill, Okla.

"As you can imagine, we have had a lot of problems after 12 years of occupation, starting with just crossing the canal," Taleb said.

But he dismissed Israeli charges of Egyptian neglect of the roads and facilities. He said Egypt had spent $15 million in northern Sinai in upkeep and improvements on the roads already returned to Egypt.

Most of this money apparently has gone to upgrade the 110-mile, two-lane highway from El Arish to Kantara on the canal, the main artery.

Taleb says the migration of Egyptians "from the valley" to the Sinai must wait at least five years until the present residents--100,000 of them Bedouins--are settled and taken care of and studies show there is enough water to support a vast population.

Instead of 800,000 acres of new irrigated land, the government now is talking about starting a much more modest project later this year that would cultivate 11,500 acres of olive and palm trees. Under the revised proposal, the U.N. Food and Agriculture Organization would provide $23 million for the project.

The biggest problem is money. Taleb said he had an annual budget of $83 million to administer and develop all of northern Sinai and would be given the same amount for the zone now being returned.

He said no special plan has been developed for the new sector and that everything would depend on the new master plan. The immediate objectives, he said, are to achieve self-sufficiency in food and to establish social services and physical facilities.

Taleb's list of the Egyptian government's accomplishments since 1979 give an idea of the region's limited capabilities: an increase in the number of drinking wells from four to 12 plus 40 irrigation wells, the new motel and airport at El Arish, an increase in the electrical power supply from one megawatt to 24, the start of 5,000 housing units and the completion of 600, self-sufficiency in poultry, establishment of 15 nurseries and four primary schools and the doubling of rooms in two secondary schools, expansion of the hospital here and the opening of nine clinics in Bedouin villages and the restoration of a 320-acre vegetable farm.

Another main obstacle to development of the Sinai has been the shortage of water. Army trucks still haul water to the Bedouin settlements springing up along the Kantara-El Arish road and oil drums serving as reservoirs stand on the shoulder.

A contract to build the first stage of a water pipeline from the Suez Canal to El Arish has just been signed after years of talking about it.

Another project to pipe fresh water through the new Hamdi tunnel under the Suez Canal into the southern Sinai remains incomplete partly because of political feuding.

After six years of construction and three inaugural ceremonies, the 2.4-mile-long Hamdi Tunnel is still not fully in use because there is insufficient electrical power for its four giant ventilators. Cars and trucks go through it in convoys twice daily each way.

Another travel bottleneck is the ferry crossing at Kantara, the main link between northern Sinai and the Nile Valley and thus between Tel Aviv and Cairo. With just one ferry in operation, with a capacity of one large bus or truck and eight cars, the wait for a crossing can take hours, especially for trucks.