THE TUMULT in Iran has reached the point where a good many people, including Iranians sympathetic to the shah, have been forced to consider whether he can hang on. Certainly, with conditions approaching something like civil war, a ruler less devoted than he to holding on to power and pushing through his ambitious modernization program might already have been tempted to anticipate a coup and seek out plush exile.Yet the shah remains on the throne, and in the light cast by the fierce challenge to him, it is possible to see with new clarity why Americans have good reason to hope he rides out the storm.

Some part of the protests against Shah Mohammad Reza Pahlevi presumably rise from the license he has given the political police, from his virtually insatiable appetite for advanced military hardware, and from the family and upper-class corruption he has tolerated if not spawned. Yet the two main sources of popular opposition are, in their separate backhanded ways, tributes to his vision for Iran.

The shah has presided over headlong econimic progress. In so doing he has excited expectations of quick individual benefit that even a far more competent government would have had trouble delivering. In modernizing, moreover, he has provoked frenzied opposition from traditional religious elements in a country long isloated and still largely rural. Those elements are opposed not just to the erosion of feudal ways but also to such basic policy planks as land redistribution and the granting of rights to women. If you throw in as well the third dimension of communist subversion - the shah, needless to say, tends to give high priority to this factor - you have a poisonous brew.

The causes of Iran's unrest are varied enough to have elicted suggestions for substantially different remedies from the shah's advisers, with military men emphasizing the immediate need for law and order and civilians tending to urge renewed attention to political liberalization. At the moment the government is on the military track, but the shah is reportedly bent on returning to the civilian track as soon as events allow. The prospect of being swept out of power by the masses in the streets is evidently less immediate to him that a right-wing coup.

Either way it would be a misfortune for the United States. For its oil, for the stability it lends to its exceedingly shaky region, for the bulwark it forms to the spread of Soveit influence, Iran matters greatly to this country. That is the rationale for the immense and pervasive American "presence" in Iran - political, military and economic. One can question whether all aspects of that presence are equally wise and necessary; one cannot deny it it exists.

It the United States is in fact committed to Iran, what makes that commitment tenable is the leadership of the shah. Unquestionably, he is more likely to go in the modernizing direction most American would like to see Iran go than any of the elements clamoring for his removal. It helps if you think for a minute of the Libyan model of an oil-rich state led by a fanatical Iranian Qaddafi. That is a distinct possibility, and one truly threatening to American interests. Without the shah, it could come to be.