Like so many things in today's Saudi Arabia, the arrival of U.S. President Jimmy Carter was a blend of the modern and the traditional, the Western and the Oriental, the mechanical and the spiritual.

The entire Saudi Cabinet, attired in traditional robes and headresses, lined up along the red carpet at Riyadh airport to greet the President. Indistinguishable in appearaance from Bedouin sheikhs of decades past, these men control awesome amounts of money and are responsible for the transformation of this primitive desert kingdom into a modern country.

There was Zaki Yamini, the oil minister, and Planning Minister Hisham Nazer, and Ghazial Qusaibi, the minister of industry. All received at least part of their education in the United States and deal with major American corporations in their daily work - just part of the reason why this country's relations with the United States are more than close. They are, as Carter said, "unbreakable.%

Behind the Cabinet officials were te stalwarts of the old Saudi Arabia - the Bedouin of the Royal Guard, dark-eyed and dark-skinned, sitting outside the room where the king was waiting, as they do in all the sheikh - doms of the Persian Gulf.Each man wore a gray robe and a bandolier of ammunition for his rifle and pistol, and in each belt was a gilded ( khanja: ), the traditional hooked dagger of Arabia.

Carter and his wife, Rosalynn, the only conspicous woman att he arrival ceremony, descended the stairs from Air Force One onto an oriental rug where they were greeted by King Khalid and Crown Prince Fahd. The king, 63, who is not in good health, carried the walking stick that is always with him now as he escorted Carter past an honor guard in Western-style uniforms of green, gold and white, while a 21-gun salute boomed in the background.

Mrs. Carter, in a turquoise suit, walked beside the crown prince and waited with him while the king and President exchanged brief greetings, all broadcast live on Saudi television. The President began his remarks with the traditional Arab salutation, ( salacmaleikum ), "peace be with you."

After sharing a cup of bitter Arab coffee in the airport lounge, the king and the President rode together to the royal guest palace in the king's black Rolls Royce.Ahead of them in the motorcade were red bereted Saudi military police in red Chevrolet convertibles, tops down.

Small but enthusiastic crowds gathered along the wide dusty streets to see the motorcade - Saudis, the Egyptian and Yemeni workmen who are transforming this desert oasis into a modern but ugly capital city, and Americans in cowboy hats and blue jeans.

In the weeks before Carter's arrival, American officials and Saudi protocol officers had long negotiations over such delicate subjects as the role of the American women visitors in a society that does not welcome female participation in public affairs and whether the American party would have to submit to customs inspection in a country where liquor is banned. (They did not.)

One matter apparently was not subject to negotiation. Less than 10 minutes after their meeting began, the king, who had been glancing at his watch, excused himself. He and a group of his retainers retired to an enormous room lined with marble columns for their evening prayers, as required by the dictates of Islam. The prayers had been listed in advance on the official schedules.

Carter was shown to his guest room, and the talks resumed when prayers ended 11 minutes later. The king stayed only half an hour, leaving the crown prince at the head of the Saudi contingent, more or less confirming the general opinion that while the king is the spiritual and symbolic head of the country, the crown prince makes the decisions.

The Carters are housed in the Naseriyah guest palace, about the size of two football fields, on the edge of town. It was built in 1956 as an administrative palace by former King Saud, who otherwise has been all but written out of Saudi history since he was deposed in 1964 by collegial decision of the royal family. He was succeeded by his brother, King Faisal, who was assassinated in 1975.

It, too, relfects some of the realities of contemporary Saudi Arabia. It is vast, ornate, splendid luxurious and run by foreigners of the staff of 170, only about half a dozen are Saudis. The rest are Egyptians, Lebanese, Sadanese and Ethiopians. The household items are imported, too, mostly from Europe, just as they are in the home of almost every Saudi who has cashed in on the oil boom.

Equally lavish and also run by foreigners is the Riyadh Intercontinental Hotel, the one first-class hotel in the capital, where the traveling press is housed. As the press arrived, the big color television sets in the press room were showing Casper the Friendly Ghost cartoons, the fare offered after the telecast of the President's arrival.