The cost of maintaining and expanding the close American relationship with the state of Israel is steadily rising. During his current visit in Washington, Israeli Prime Minister Yitzhak Shamir is expected to seek more than the $910 million in economic aid recently approved by Congress for fiscal year 1984. He would also like to reduce the amount of US military assistance approved - $1.7 billion - to about $1.275 billion but have all of it in the form of outright grants, rather than in loans.
The Reagan administration has agreed to accept this proposal because it wants to revamp military aid to a number of countries that are having difficulties repaying their loans. Apart from foreign-policy and economic considerations, a larger free dole to Israel could also gain political benefits among the American-Jewish community.
Only six years ago, total annual aid to Israel amounted to $1.785 billion. It rose to $2.1 billion in 1981 and to $2.485 billion in 1983. The 1984 package passed by Congress in its continuing budget resolution amounts to $2.6 billion. All of the so-called economic support aid ($910 million) and one-half of the military assistance ($850 million) are straight grants - no repayment needed. The rest of the aid is a soft loan, payable over 30 years with no payment on principal required for 10 years.
Since 1962, the United States has given Israel about $25 billion in aid, half of it a gift.
What is significant about the growing Israel aid budget is that Congress is more generous toward Israel than is the President. Mr. Reagan requested that only $550 million of the military aid for 1984 be in grant form.
The lawmakers raised this sum by $300 million on grounds it would be ''unrealistic'' to give Israel less than the $750 million in military grant aid it received in fiscal 1983.
If Mr. Reagan accepts the Israeli request for more favorable aid terms, he could add as much as another $300 million in nonrepayable military assistance.
Also, the Congress has approved use of American military aid for development of Israel's fighter airplane, the Lavie (lion), despite the fact that it will compete with US planes on the world market. American manufacturers are concerned , because they receive no such equivalent government help.
To what extent domestic political considerations drive the Reagan administration's policy toward Israel is difficult to determine. The traditional wisdom is that presidents do not like to be seen opposing or criticizing Israel in a politically sensitive election year.
''In a year preceding an election, all issues having political implications become more sensitive,'' says one observer. ''Under those circumstances, the President may be more cautious in taking initiatives that could hurt him. But no president would play with basic American interests because of domestic political considerations.''
Some experts say they believe that the current US impulse to get closer to Israel is less the result of pressure from the American Jewish community on the White House than of a genuine frustration on the part of Mr. Reagan's aides - especially Secretary of State George P. Shultz - with the stalemate in the Middle East and a desire to try a different tack. Hence the effort now to make a tactical shift that may force Syria and its Soviet patrons to negotiate.
''The realities of the Middle East are the cause of his (Shultz's) conversion ,'' comments an experienced analyst.
Diplomatic experts point out that, when a situation demands it, a strong president can set a firm policy without feeling politically intimidated or suffering any domestic political fallout. President Eisenhower in 1956 took an uncompromising stand after Israel invaded Sinai, forcing it to withdraw, and went on to be reelected.
''The president can take a position that Israel opposes if the American people as a whole are behind him,'' comments an aide in the Carter administration who had dealings with the Jewish community. ''Then the Jewish community will support him also. That happened with Ike and the Sinai, and it is still true.''
Experts say the difficulty lies in sustaining a firm policy over a long period, especially in the face of congressional resistance.
As Congress has grown more assertive in the foreign policy field, it has also acquired more influence on Middle East policy, including arms sales and aid to Israel and the Arab countries.
''Congress has set the parameters in which the administration operates,'' says a knowledgeable observer.
Democratic lawmakers in particular are disinclined to buck the pro-Israel lobby.
The Democratic Party is said to receive about 50 percent of its funds from the Jewish community, and at election time this is a definite factor in the consideration of foreign policy questions, including aid to Israel.
Presidential candidates also feel under contraint not to alienate the American-Jewish vote. Sen. John Glenn of Ohio seemed to make a 180-degree turn from his traditional Middle East positions in a recent speech when he criticized the Reagan administration for being too tough on Israel.
According to political observers, a principal objective of the senator was to attract Jewish financial and political support in such key states as New York, California, Ohio, and Florida.
More than sheer politics is involved in aid votes, however. Experts note that the pro-Israeli lobby, the American Israel Public Affairs Committee, has a potent voice because it is able to coalesce support for Israel which already exists.
Liberals and conservatives in Congress, as well as the American people in general, have a strong affinity for Israel related to the Jewish Holocaust and the view that Israel is fighting for its survival. The fact that Israel is a democracy and that it is perceived as a deterrent to Arab adventurism and Soviet expansionism is an added element in the consistent American support for Israel.
Whatever the tactical shifts of US policy, experts see no fundamental change in America's commitment to UN Resolution 242, which calls for a withdrawal of Israel from occupied Arab lands in return for peace. Some voices in the American Jewish community say they believe that the 242 approach has not been successful and that other ideas should be tried. But the administration has consistently backed 242 as the framework for a negotiated peace.
The question is how forcefully the Reagan administration will pursue implementation of 242, an issue that was neglected in the first two years of Reagan's term and then superseded by the Israeli invasion of Lebanon and subsequent events there.
Some experts say that the President, even in an election climate, could link aid to Israel with the issue of Jewish settlement policy on the West Bank if he were willing to take the lead - and the political heat.
''This could be dealt with, but the President would have to make the settlement issue a top priority, and few presidents can be convinced to give it that,'' says one analyst. ''Reagan will cave in on aid even though he should not give more - for Israel's good as well as foreign policy reasons.''