President Reagan's long-awaited proposals yesterday on strategic nuclear weapons for the future ended one set of costly political problems for the White House but may begin another: an unaccustomed confrontation with some powerful conservatives in Congress and military strategists.

The president's plan would produce a quick increase in U.S. atomic striking power and get rid of the various controversial "shell game" proposals for shuttling new MX missiles among hundreds or thousands of protective shelters in Utah, Nevada or other western states, thereby theoretically hiding them from the Soviets.

But the president's alternative of deploying MXs at least initially in remodeled protective silos now used for old Titan missiles has drawn instant condemnation from some powerful Republican leaders in Congress and could set off sharp debate among military strategists.

The critics say the administration has dropped a missile-basing plan chosen by the Air Force after exhaustive study in favor of one in which the MX, at least initially, would be more vulnerable to attack.

A visibly upset Sen. John Tower (R-Tex.), who is chairman of the Senate Armed Services Committee, told reporters he is "gravely disappointed" in the president's decisions, especially on the MX, and that Reagan's defense program may not be as strong as that left by President Carter. Seemingly stung by a lack of consultation on the final decision, Tower said that Reagan's decision "appears to have been made within a small circle without the coordination of the best technical and military experts."

Rep. William L. Dickinson (Ala.), ranking Republican on the House Armed Services Committee, also said in an interview that he was "very disturbed on the MX. They pretty well negated all the experts we've heard from for the last five years testifying before our committee . . . a lot of people who put their professional careers on the line and provided a lot of facts." Dickinson was referring to Air Force officers and others who have consistently rejected other MX deployment schemes in favor of the various shell games.

In announcing the plan to use the Titan bases for MX yesterday, Defense Secretary Caspar W. Weinberger described it as a "near-term" solution and in effect acknowledged that after nine months of intense study, the administration still has not figured out what to do ultimately with these huge and controversial new weapons. "We have concluded that there is no single best system that we know of right now," he said.

The administration believes that the decisions outlined yesterday are the best possible in a situation where there are no clear, easy answers.

In turning to Titan silos, reinforced with extra cement and steel to make them harder for Soviet missiles to knock out, the administration can offer a home to the first 36 or so MXs scheduled to come off the production lines in 1986. This means the missiles -- each of which will carry 10 nuclear warheads in its nose and which is supposed to be extremely accurate -- will become immediately operational and give the United States more of the same kind of potential first-strike firepower that the administration claims the Soviets already have.

Much of the debate on basing the MX has centered on how to protect the missile against a Soviet first strike. But the Reagan administration has made clear it also has a corollary objective: to force the Soviets to worry about the same threat. Weinberger alluded to this several times yesterday, suggesting there was a need for the power and accuracy of the new missiles, for deterrence, to prevent nuclear blackmail or intimidation, and to strengthen the U.S. hand at any forthcoming arms control talks.

Adding the 10-warhead MX to the existing 1,000 Minuteman missiles, which carry between one and three warheads each, also means more U.S. missiles would survive a Soviet first strike.

Similarly, on the B1 bomber, the administration argues that it is too risky to wait for the new advanced "Stealth" bomber that may or may not live up to expectations and that the venerable B52 is getting old in the meantime. In effect, both the MX and B1 decisions represent a gamble that having new weapons in the pipeline, even though there is controversy about their effectiveness, is better than waiting and studying some more.

Weinberger and his aides argue that rebuilding the Titan silos to better withstand the intense blast and pressure of an attacking atomic warhead will buy at least a few years of extra survivability for MX, perhaps to the end of the decade. This is because Soviet missiles would have to score a direct hit on the silos in order to knock them out and the Soviets missiles are not yet that accurate, officials claim. Within those extra years, the Pentagon would try to figure out what to do with the rest of the 100 or so MXs to be built.

The problem, however, is that years of Air Force testimony in Congress and elsewhere has, as one senior officer put it, "generally rejected quickly" the idea that super-hard silo plans would be effective.

Tower charged the Titan silos would present Moscow with "a more lucrative target in already vulnerable fixed silos." The administration argued that the old Carter plan of shuttling 200 missiles among 4,600 shelters or a newer option of 100 missiles and 1,000 shelters would be overwhelmed by the Soviets just adding more warheads. But with fixed silos, the Soviets could concentrate dozens or more warheads on a single fixed location.

Weinberger claimed yesterday that "these decisions, and I'm sure nobody will believe this, were absolutely based on the best kinds of professional advice and examination of the objectives." Yet the decision clearly runs counter to the multiple-shelter shell game the Air Force wanted and that was also reportedly recommended, together with an anti-missile defense system, by the prestigious Defense Science Board of outside experts. Similarly, the silo-basing interim solution also is not believed to have been part of recommendations by the special Townes commission set up by Weinberger in March to suggest alternatives.

Reagan's decision was an extremely well-kept secret, not only from the nation's media but also from scores of people working on the defense program in government and Congress. In the past week or so, it was clear that only a half-dozen people including the president knew what was really happening and while this may have prevented leaks, it also left many officials, senior military officers and lawmakers surprised and unhappy and may weaken the administration's position internally. Top-ranking Air Force officers, for example, did not know how their major new weapon for the 1980s would be based until just hours before the decision was announced.

Nevertheless, for the White House the MX decision has major political pluses, aside from any military advantages administration officials see. By junking even a scaled-down shell-game plan, the White House avoids the trap of having it said it was advocating only a scaled-down version of Jimmy Carter's MX scheme, after having denounced Carter as weak on defense in last year's campaign. The irony, however, is that the MX shell game idea goes back to the Ford administration.

Similarly, the administration does not have to contend with the powerful Mormon Church, which has headquarters in Utah and made clear it didn't want MX.

The president avoids offending his closest friend in the Senate, Republican Paul Laxalt of Nevada. Laxalt, who many lawmakers believe was a key figure in the decision, and Sen. Jake Garn (R-Utah) came out publicly in June for a system of basing MX in existing silos that is very similar to the one chosen.

Financially, officials claimed yesterday there is also a considerable savings in the budget, at least for a while, in dropping the vast new construction project of hundreds or thousands of concrete garages throughout the southwest that would have been needed for the shell game.

The idea behind the shell game was that it would confuse Soviet targeters because they would never know which shelter held an MX missile and thus they would have to expend hundreds or thousands of missile warheads to hit them all. While critics of the Reagan package may contend that the new solution is worse, the shell game itself, even in a scaled-down version, was never very popular. It always had a Rube Goldberg quality to it, was extremely expensive, and suggested an interminable shelter-warhead construction race between the United States and the Soviet Union.

Still, the administration essentially admits that it doesn't know what should be the permament solution. By 1984, it is supposed to decide whether to build extremely deep underground silos, perhaps on the south sides of mountains where they would be very hard for Soviet missiles, coming from the north, to hit. The idea here is that these missiles could come out of their holes days or weeks later to retaliate if necessary against Moscow. But there are only paper studies of such basing concepts today and no guarantee these will one day look like a good bet.

Another alternative is a favorite of Weinberger's: putting the MX into big new transport planes that can stay aloft for days. This is even more strongly opposed not only by the Air Force but also by the State Department, which fears it will lead Europeans to eventually rejected accepting American missiles on their soil because Americans won't put new missiles on U.S. soil.

The third alternative is to build anti-missile defenses to defend the silos. But as Weinberger acknowledged yesterday, anti-missile defense technology is simply not good enough today to be confident it will knock down even half of the incoming warheads. Even batting .500 is not good enough in that league, Weinberger told reporters.

So the idea is to buy time while these alternatives are intensively studied to see if they will work. If there is a second Reagan Administration, the ideas may be put into operation. If thee is a new one after 1984, it is conceivable that the strategic issues will turn down still another road.