There are about a dozen anti-tank weapons in the Reagan defense budget, and together they provide a metaphor for the president's effort to rearm America.

Research and development on most of them, including many of the more expensive and exotic, were begun in the Carter years and earlier, long before Ronald Reagan came to office.

But the military services have often done simultaneous research on a number of weapons with similar purposes in the past. Then the secretary of defense, or the Office of Management and Budget or the president himself would choose among them, selecting perhaps only one or perhaps two for production.

Reagan has done much less selecting. His approach has been not only to go ahead with almost all the weapons, but to increase their rates of production.

A recent study in Armed Forces Journal of all basic Army procurement programs showed them running 20 percent or more ahead of the rates last projected under Carter. That kind of heavy spending has led some critics to denounce Reagan's defense budget as throwing money at problems, letting the services have free rein.

"Reagan opened the door for the military services so they plunged for everything they could get," William Kauffman, budget adviser to four secretaries of defense before Caspar W. Weinberger and a professor at Massachusetts Institute of Technology, said in an interview recently. He called the weapons purchasing in the Reagan budget "rather indiscriminate."

But the services would far rather have too many weapons than too few.

For years the Army and Air Force have been trying to develop weapons to combat what they regard as the serious Soviet tank threat in western Europe. They say the Warsaw Pact nations have three times as many tanks as NATO does in the European theater. They see these tanks as the leading edge in any Soviet military attack against the West.

Their most basic step has been to develop and begin producing a more formidable tank of their own, the M1.

At the other end of the spectrum, they have also supported development of a new and supposedly selective kind of nuclear weapon for use against tanks. In theory, these neutron weapons would neutralize Soviet tanks in Europe without also leveling European cities.

But most of the Pentagon effort has been to develop weapons of an intermediate sort--systems for firing crippling rockets or missiles at enemy tanks from far enough away to be relatively safe but still absolutely accurate. Over the years the services have thought up a series of such weapons, ranging from glorified bazookas to laser-guided missiles fired from helicopters to smart bombs dropped by planes.

Here is a list of these weapons. Most are in the Reagan budget. As a group they may offer some insight into how that budget was built. It is not all-inclusive. For example, the Army has anti-tank artillery shells and both it and the Air Force have anti-tank mines.

The most basic weapon is called LAW. It is an eight-pound, single-shot, Norwegian-made infantryman's weapon with an effective range of about 100 yards--a modern version of the old World War II bazooka.

The good news is that it does not cost much; the last 100,000 purchased "a few years ago" cost about $200 each, an Army spokesman said. The bad news is that it cannot penetrate a Soviet tank's front armor; it can only cause damage if it hits the tank from the side, on the tracks, or in the rear where the armor is weakest.

Because of LAW's weaknesses, the Army in the mid-1970's began looking for a successor. General Dynamics, the nation's largest defense contractor, offered to build, at $78 per copy, a single-shot disposable tank killer called the Viper which would weigh seven pounds and have a lethal range of more than 200 yards.

In fiscal 1981, the Army okayed production of the first 1400 Vipers, out of what it hoped would eventually be almost a million at a cost of $1.2 billion.

But today the Viper, too, is in limbo. The first test models were rejected, then redesigned. The Army now estimates cost per copy at $800 to $1300, more than 10 times greater than originally promised, and recent tests show it is not performing up to specifications.

Though it does have both a more powerful warhead and greater range, the Viper cannot destroy a Soviet tank head-on. But the Army still wants it and is touting its usefulness against the more lightly-armored Soviet BMP armored personnel carrier and reinforced cement buildings.

The Dragon is the next largest anti-tank weapon. Carried by one man whose only job is to fire it at tanks, it has a range of roughly 1,000 yards and is wire-guided, which means the gunner must remain in position after firing and keep the target tank in his sight until the projectile hits. That could leave him exposed to fire for about 30 seconds.

A newer version of the Dragon, called the Rattler, is now in research and development. It will have greater range and, to help protect the gunner, a lower "launch signature," meaning it will be harder for the enemy to see the Rattler fired and fire back.

Perhaps the best anti-tank weapon in the Army is the next on the list, called TOW, a launcher whose projectile with its rocket motor can be lethal to tanks from 1,000 to 3,500 yards. It too is wire-guided and so has an exposure problem.

Because it is so reliable, however, the TOW has been mounted on several land vehicles and helicopters. There are some Army officers who say the controversial $1.9 million Bradley infantry fighting vehicle would have been dropped long ago if someone had not come up with the idea in 1976 of mounting two TOWs on it to give it a tank-killing capability.

The TOW also has been mounted on the Cobra helicopter, which can carry eight of its missiles. The Cobra, however, needs to hover over the battlefield in an exposed position while the airborne gunner guides the projectile to the target.

Meanwhile, according to the Army, work is under way on an improved warhead for the TOW II, which will be larger and thus able to penetrate new Soviet tank armor. In addition, a thermal night sight for the TOW is being explored, one that picks up heat signals.

And, in the most exotic permutation to date, work is under way on anti-tank weapons using not wires for guidance, but lasers. The virtues of such a system are obvious. As long as the beam is on the target, the projectile cannot miss.

But the disadvantages also are powerful. For one thing, as with the wire-guided systems, someone, or something, must serve as a designator and hold the beam on the target, leaving himself in jeopardy.

There are now three proposed designation systems. The only one in production involves a soldier on the ground operating a ground laser locator designator (called a GLLD). The other two involve putting designators in helicopters or unmanned aircraft called remotely piloted vehicles or RPVs.

The lasers also have this problem: they cannot, at present, work through smoke, dust, fog, heavy rain, snow or normally at night. Critics say this means they would be of little use on a battlefield in western Europe, where only a third of the days are clear.

The Defense Department's research agency is working on an all-weather laser.

Meanwhile, it has moved forward in recent years to begin production of two expensive laser-guided anti-tank weapons systems, the Hellfire missile to be carried aboard helicopters and the Copperhead projectile to be fired from a 155-millimeter artillery piece.

The Army's experience with the Copperhead illustrates the problem of pushing high technology too fast. The original program called for 110,000 shells at roughly $15,000 each; the cost was justified by the promise of a 90 percent kill ratio.

But this promised accuracy did not materialize. When production started in 1979, the Copperhead scored below 80 percent in hits on tests. Efforts to increase accuracy also increased costs. By early this year, the Army was planning to spend the same amount, but was saying it would buy only 44,000 shells.

When the Copperhead scored only 67 percent on new tests in August, Congress finally lost patience. Reagan's request for additional production funds was refused and the Army was told to stop production at the 8,000 Copperheads already funded.

The Hellfire illustrates another type of problem the Army faces. The helicopters that would carry the missile would be vulnerable if they crossed into enemy territory because the Soviets have both sophisticated aircraft and ground weapons that could shoot them down.

To carry the Hellfire, the Army has developed the AH-64 Apache helicopter. Its cost has more than doubled over the past few years to $16 million per machine. The Apache has two extremely powerful engines and can climb quickly in both hot desert and cool northern climates. It also is capable of carrying 16 Hellfires and firing day or night in all types of weather thanks to a sophisticated, and not yet refined, infrared sighting system.

Because it costs so much, however, the Army has worked out tactics so that the Apache itself would not have to act as designator for its Hellfire missiles. Instead, as Army officials have told Congress on several occasions, the Apache will just pop up, fire its Hellfires and drop down again so that it will not be exposed to enemy fire.

That means, however, that the laser designation must come from elsewhere. The favorite current candidate is yet another helicopter, still in development, called AHIP. The AHIP is a modern version of the present OH-58 Scout.

Its cost, too, has grown in the past two years from roughly $700,000 per machine to about $2 million. And its cost may rise even further because the Army has decided it must place the laser designator for the AHIP in a mast that will be constructed above the rotary blades. This will theoretically let the AHIP designate as it, too, hides behind trees with the mast sticking out above the branches, much as a submarine periscope rises above the sea so it can see the ships it aims at.

Since both the Apache and the AHIP would have to remain on the NATO side of any battlefield to avoid being shot down, they could only be used against tanks that could be seen across the front lines, or tanks that had broken through into friendly territory.

Even with these limitations, the $7.4 billion program to buy 446 Apaches is under way along with the $3.2 billion AHIP program.

The Army has also had trouble developing a system for locating enemy tanks behind the front lines, vital information if it is to use any laser systems.

For two years, an Army project called SOTAS was being funded. It was based on putting sophisticated look-down radar aboard helicopters which would find the target tanks and report back via a complicated computerized communications system.

The projected costs of SOTAS soared last year from under $1 billion to over $3 billion and Congress killed it.

Like the Army, the Air Force has been running into problems in developing its anti-armor program.

The most controversial of the Air Force anti-tank weapons is the Maverick missile. They are guided by television from the cockpits of Air Force planes; today some 200,000 are stockpiled in Europe. The trouble is that some key Air Force generals do not believe a television guidance system would work any more than a laser system in the inclement weather found in Europe.

The Air Force, itself, is at work on a more modern version that has an infrared guidance system that zeros in on heat sources. As of May, the service was going to buy 42,275 of these new missiles at a total cost of $2.97 billion.

By September, however, cost estimates were such that the Air Force was planning to buy only 30,000 Mavericks for the same amount; cost per missile had risen 23 percent over those four months. Serious question also have been raised as to the accuracy of the new Mavericks. Enough doubt was raised to delay full-scale production for more than a year while additional testing takes place.

The Air Force also has run into problems with another of its more exotic new weapons systems, the anti-armor cluster munition (ACM), which consists of a bomb which, when dropped over a target, explodes and releases 48 separate submunitions. These bomblets would float down and attach themselves to the tops of tanks, the weakest spots on the vehicles. They would then explode through the metal, sending a red-hot projectiles into the body of the tank.

Last month, the Air Force held up a production decision on the first 2,000 at a cost of $54 million, or $27,000 apiece. The test program, the Air Force told Congress, had not provided "a sufficient data base" to make such a production decision. It is now expected early next year.