The Senate last night overwhelmingly registered its disapproval of one of the main new strategic weapons proposals of President Reagan, adopting 90 to 4 an amendment designed to keep the Pentagon from spending research funds on an interim plan to house MX missiles in hardened silos.

The carefully worded amendment, which does not foreclose eventual use of hardened silos in a permanent basing scheme for the missiles, marks the first time the Republican-controlled Senate has opposed the administration on an important defense question. Amendment sponsor William S. Cohen (R-Maine) said the vote was intended as a message to the administration that it should immediately consider other basing options, including a variant of a so-called "shell game" mobile scheme that was proposed by President Carter.

The issue of basing the MX has been one of the nettlesome problems Reagan has faced in the first year of his presidency. During the 1980 campaign he assailed Carter's proposal to rotate 200 MX missiles among 4,600 cement shelters in Nevada and Utah, and since becoming president Reagan has been under heavy political pressure not to dig up those two states.

In October, as part of a broad strategic defense plan, he proposed building 100 MX missiles, housing the first 30 to 40 in existing silos and developing a permanent basing system by 1984.

That plan took heavy flak from pro-defense congressmen who remembered years of military testimony on the Hill that placing the MX in an unprotected, immobile silo would not close the "window of vulnerability" of which Reagan made an issue in the 1980 campaign.

The amendments being considered by the Senate are to the $208.5 billion defense appropriations bill.

The bipartisan amendment voted on last night is considerably less restrictive than one to be offered today by Sen. David H. Pryor (D-Ark.) that would delete all fiscal 1982 research funds for hardening silos for the MX. Even so, last night's action made it clear that any plan to place the MX in fixed sites will have a difficult time. Cohen called the fixed site proposal "unsuitable," and his co-sponsor, Sen. Sam Nunn (D-Ga.), said it was "the most ill-conceived and ill-advised" portion of the president's strategic defense plan.

There was no immediate response from the administration. However, Sen. Ted Stevens (R-Alaska), chairman of the defense appropriations subcommittee, said he had informed Secretary of Defense Caspar W. Weinberger of the proposal and, "while I can't say he is overjoyed at the direction of this amendment, I think he understands the reasoning behind it."

Nunn, considered one of the Senate's leading defense experts, said during the debate last night that any plan to place a new weapon system in a vulnerable basing mode would be "destabilizing."

"I would not want the word to go out that we are moving to a launch-on-attack" strategic posture, Nunn said. He added that expert military testimony had convinced him that hardening the Titan and Minuteman silos with concrete to withstand 5,000 pounds per square inch of pressure would not make them any less vulnerable to Soviet warheads. Placing the MX in such silos might put the country in a "use them or lose them" posture if the Soviets launched an attack.

His sentiments were echoed by a number of Republicans. Sen. Mark Andrews of North Dakota said that "this whole MX thing borders on the silly . . . we're buying a Rolls Royce and we don't have a garage to park it in."

Throughout the debate, supporters of the Cohen-Nunn amendment voiced support for the missile itself, a four-stage rocket that would carry 10 nuclear warheads, each capable of separating from the missile in space and dropping on a different target. The 100 missiles are planned for deployment in the mid-1980s.