Menachem Begin's strategy for Israel ran out this past week along with his tenure in office. He cited personal reasons for resigning the prime ministry of Israel. But his resignation also was a logical reflection of the fact that his policies are stalemated.
Here is the dilemma he leaves for his successor.
He dare not withdraw his armed forces entirely from Lebanon because to do so would be to confess that the invasion of Lebanon had been an expensive mistake both in human life and to the economy of Israel. But to keep his forces in Lebanon, even on a shortened line, would mean continued casualties and a continued drain on the Israeli economy.
Public tolerance in Israel for more casualties has been strained to the limit. The economy has been loaded to the point where national bankruptcy can be averted only by an increased subsidy from a United States which is beginning to question the present level of its annual grants and loans to Israel.
Perhaps the supreme anguish in the situation, for Mr. Begin and for his successor, is that the key is now held in the Kremlin, with which Mr. Begin has been waging a cold war ever since he took office, rather than at the White House in Washington, where his influence is still substantial.
His invasion of Lebanon would have been a decisive success and the crowning achievement in his career if Syria had been willing to acquiesce in a peace between Israel and Lebanon that would have left the government of Lebanon as a client state in the Israeli system.
Amin Gemayel of Lebanon signed such an arrangement with Israel. Under it, Israel would have retained military influence in a ''security zone'' in southern Lebanon plus entry into the economy of Lebanon. Lebanon would have become partly dependent on Israel, both militarily and economically.
That in turn would have given Israel peace and security on all its frontiers, plus a clear road to the decisive annexation of the occupied territories - West Bank, Gaza, Golan Heights, and East Jerusalem.
But Syria refused to acquiesce. And Syria's refusal is backed by the Soviet Union, which has recently completed the military resupply of Syria along with supplying several thousand Soviet military personnel to man the new weapons and train the Syrians.
Israel invaded Lebanon without encountering Soviet troops. A year ago Israel could have done the same in Syria. But that time has gone by. To invade Syria now would be to encounter Soviet troops and to put Israel effectively in a state of war with the Soviet Union. Three conditions, any one of which would be decisive in itself, rule out an Israeli war against the combination of Syria and the Soviet Union.
Israeli public opinion could not tolerate another military campaign after the results of the campaign in Lebanon. The Israeli economy could not stand another such campaign. The White House could not allow Israel to attack Soviet troops. No matter how much Washington favors Israel it is not prepared to go to war with the Soviet Union for the sake of any Israeli territorial expansion.
In other words, Moscow, by resupplying Syria with modern weapons and by sending Soviet troops with them, has stalemated Mr. Begin and Mr. Begin's strategy. And in the process Moscow has also improved its position in Arab eyes as their champion and defender against Israel.
The United States, on the other hand, has lost status in Arab eyes. White House acquiescence in Mr. Begin's invasion of Lebanon has wiped out the comparatively ''evenhanded'' position that Washington occupied during the Kissinger-Brzezinski phase in American foreign policy. That was what enabled the US to broker a peace settlement between Israel and Egypt. Today, no Arab government would trust it to be an honest broker.
The only way the US could regain its lost middle position in the Middle East would be to decree an immediate halt to the building of Israeli housing and settlements in the occupied territories - and make it stick. That could help restore the American position in Arab eyes.
President Reagan, on Aug. 27, asserted that his Middle East plan of a year ago is still alive and valid. He said that the continued building of the settlements by Israel is ''an obstacle to peace.'' He said he is ''concerned over the negative effect'' of the settlements. But he did not say they must halt.
Meanwhile, the one thing he can offer the Arabs that would bring them to the peace table is disappearing: a place where Palestinians could enjoy some form of self-rule within a general peace arrangement. Credibility is being drained out of the US position by Israel's continued building of modern housing on the West Bank. The only way to restore the lost American brokerage position in the Middle East is to stop the building.
Ironically, it is the very Begin policy of building housing for Jews in the occupied territories which has deprived Washington of the ability to help Israel find the road to peace with its Arab neighbors.
The bottom line under it all is that Israel is now dependent for its survival on a steadily rising US annual subsidy. It cannot maintain its armed forces, its embattled military position in Lebanon, and the standard of living of its people on the present American subsidy. Much of the present array of grants and loans now goes for service of the existing debt.
Mr. Begin's strategy has brought Israel to the point where it can neither wage more war nor make peace. It is a predicament his successor will now have to grapple with.