Saudi Arabia is running short of cash.

Unlikely as it seems although the world's leading oil producer isn't likely to go broke anytime soon, it dies have a serious cash-flow problem - at least temporarily.

As a result, the government has begun a significant belt-tightening program to help make ends meet.

Beginning in May, the Saudis started quietly cashing in short-term investment's such as bank certificates and notes that they previously had been renewing automatically.

Latest estimates are that the total transferred from portfolios to government coffers since then may have exceeded $12 billion.

Other Arab oil-producing nations are said to be in a similar bind.

The reason for the Saudis' financial problems has been the worldwide oil glut, which has dampered demand for crude and forced sizable production cutbacks throughout the oil producers' cartel.

Today, the Saudis are producing about 7 million barrels of oil a day, well below the 85 million-barrel-a-day pace needed to bring in enough revenues to keep the government's budget balanced.

During boomier days, the Saudis had imposed an 85 million-barrel-a-day ceiling on their production, in part to mollify Arab critics who wanted lower output lavels and higher prices.

At one point last summer, Saudi production levels dropped to 6.7 million barrels a day.

In a face of all this, the Saudis have run into a sizable - albeit temporary - cash-flow squeeze. Sources say the transfer of funds out of shortterm investment and into the treasury has reached several million dollars a day.

The difficulty is strictly a cash problem and has not yet affected the Saudis foreign exchange position. Official statistics show the Saudis still have $26 billion in foreign exchange, and private estimates double that.

U.S. officials have forecast that the Saudi's trade-and-investments surplus will drop to $18 billion this year, declining further in 1979 and beyond. Overall, there is no evidence the country is going under financially.

Nevertheless, the cutback in oil revenues has forced some visible belt-tightening in recent months. Besides cahing in some of their short-term investments the Saudis also have cut back in other areas.

At the start of last summer, the Saudi Council of Ministers ordered a $4.5 billion spending cut that amounted to 10 percent of the government's total budget. Since then King Khalid has boosted the reductions to one-third.

On the royal family's order, the government held up for two months a relatively modest $400 million in advances to contractors for a $2 billion gas pipeline being built from the Abqaiq oil field to the industrial city of Yenbu.

Recently, the Saudi Finance Ministry proposed that the Arabian-American Oil Co., of which the Saudis own a majority and are negotiating to take over, finance all of its big new expansion program from a scant 50 cents a barrel on oil sales.

If the Saudis hold firm to that restriction, it could slow plans to enlarge Aramco's production capacity. Current programs are aiming for a 12 million-barrel-a-day capacity, up fro 10.5 million now.

What makes the problem so touchy is that there is nothing very dramatic the Saudis can do about it.

As U.S. officials argued to Khalid last month, any sizable increase in oil prices now could hurt major Western economies and send the dollar plunging further. Ultimately, it could dampen demand for oil even more.

The Saudis also could cut back on foreign imports, which have mushroomed since the Arab oil embargo five years ago. That would mean curtailing new industrial development programs - a step they are reluctant to take now.

A third option would be to step up their oil production, either by boosting the cartel's overall output or by insisting on a larger share of the cartel's total production.

Analysts say the difficulties now being faced by the Saudis could have broad implications for other Arab nations and for the effectiveness of the oil-producing cartel as a whole.

In the past, the Saudis have played the swing-man in the cartel, trimming their production levels in order to bail out other producers without raising the overall price of oil. That kind of "absorption" now seems at an end.

How well the Saudis will be able to cope with the current squeeze may depend on several factors, the most important of which is whether the world oil market firms enough. Recent weeks have shown firming in spot markets.

For now, most analysts believe the cash-flow squeeze the Saudis are in will be temporary, and that the budget-paring done so far will be enough to ride the government through to a reversal early next year.

The oil-producing nations have scheduled a meeting at the end of this year to decide whether to raise prices in January. In anticipation, the major oil companies are expected to step up their purchases, aiding the Saudis some.

Like the United States, the Saudis easily can defer millions of dollars in relatively minor construction projects without jeopardizing construction of major port facilities, so little serious disruption is expected.

Meanwhile, however, the cash-flow problem is bolstering the views of some analysts that the oil producers' cartel someday may begin to show signs of cracking.

While the present dilemma is far from a turning point, economists point out that the cash squeeze finally is forcing the Saudis to consider boosting production levels - a move that should help avert a major price increase.

If th oil producers can't work out the problem of how to divide their shares of the oil-revenue pie, it could spur private discounting or other sales gimmicks - all to the benefit of oil consumers.