President Carter announced yesterday that he has approved a plan to base the new MX missile in clusters of underground shelters in Utah and Nevada that will be connected by surface roadways, or "race tracks," allowing the missiles to be shuttled quickly from one shelter to another.

The president's long-awaited decision will cost an estimated $33 billion over the next 10 years for development of 200 of the new generation long-range missiles and construction of their bases on government-owned land in the two western states.

In announcing his decision to reporters yesterday, Carter said the basing plan he approved will make the missiles less vulnerable to attack while still complying with the terms of arms limitation agreements with the Soviet Union.

But, he added, "this system is not a bargaining chip" for future negotiations with the Soviets. "It's a system that America needs and will have for its security. I'm confident that the American people will support its deployment," he said.

The president's announcement brought quick criticism from organizations that oppose the MX missile, regardless of where or how the missile is deployed.

Jeremy J. Stone of the Federation of American Scientists called the MX decision "not just an inflationary, multibillion-dollar strategic mistake but an arms control disaster." Stone argued that the new missile will prompt the Soviets to build more missiles and said there is "no strategic need to imitate the Russian preference for large land-based missiles."

A spokesman for the Coalition for a New Foreign and Military Policy predicted that the basing plan may help prevent deployment of the missile because it will be seen as an expensive, environmentally damaging "Rube Goldberg scheme."

The president decided in June to approve development of the MX, a 190,000-pound missile capable of carrying 10 nuclear warheads. But he deferred at that time a decision on how the new missiles would be based.

MX development is designed to counteract what defense planners consider the growing vulnerability of the United States' force of 1,000 Minuteman and 54 Titan land-based intercontinental ballistic missiles. These missiles, based in fixed, underground silos, are considered increasingly vulnerable to attack by more powerful and accurate Soviet missiles capable of delivering large nuclear warheads.

Numerous schemes were considered to achieve two seemingly contradictory objectives in basing the MX: to be able to conceal the missiles, making them less vulnerable to surprise attack, while still allowing the Soviets periodically to verify the number of MX missiles in the U.S. arsenal.

The plan Carter finally settled on is known as the "race track" concept. Under it, each of the 200 missiles will be partially assembled in the open, allowing the Soviets to know how many the United States has built.

Each missile will be loaded on a huge transport vehicle and concealed by a shield. In turn, the transports will be placed on surface roadways, designed like a race track, and connected by spur roads to 23 shelters that are similar to underground parking garages.

According to the plan, transports will shuttle each missile among its 23 shelters -- each separated by about a mile -- while the Soviets remain uncertain which shelter actually holds the missile. But the shelters will be able to be uncovered periodically, allowing the Soviets to verify that there is no more than one MX missile for each 23 shelters.

Preliminary Pentagon planning calls for 40 such MX installations, each consisting of five "race tracks" of one missile and 23 shelters. In all, according to Defense Secretary Harold Brown, the massive project will involve 200 missiles and transports, 4,600 underground shelters and 10,000 miles of roadway.

Brown said most of the MX installations, including the roadways, will remain open to the public. But the shelters, which will cover a total of 25 square miles, will be fenced off and closed to the public, he said.

Brown said state officials in Utah and Nevada support the basing scheme. He said the system's advantages include the fact that the missiles, if necessary, could be fired directly from their transports on the roadways, or could be moved from one shelter to another even after the Soviets had launched a nuclear attack.

"This system is such that the Soviets will have a very difficult time planning attacking it," he said.

The president said that in making the basing decision he had five objectives. He said he sought a system that would enhance the ability of U.S. missiles to survive an attack, would be verifiable by the Soviets, would have a minimum impact on the environment and a "reasonable cost," and would be consistent with U.S. goals to negotiate a reduction in the number of strategic nuclear weapons.

The "race track" scheme, Carter argued, "does the best job" of meeting the growing Soviet threat and those objectives.

Deployment of the MX remains subject to congressional appropriations. Brown said the first test flight of the missile is scheduled for 1983, with initial deployment of the weapon set for 1986 and full deployment by 1989.