President Reagan is being told privately that Soviet President Leonid I. Brezhnev's unusual speech last week to his military commanders shows that the Soviet Union is on the defensive in the arms race and is laboring under the strain.

To the president's more militant advisers, that represents cause for American satisfaction, justifying even more pressure on the Soviet Union. It shows, they maintain, that the Reagan military buildup is "paying off." The Soviet Union "is hurting," one senior adviser said, "and that is good."

But that is not the assessment that has emerged publicly.

For public purposes, the administration put an almost exactly opposite characterization on Brezhnev's Wednesday speech. The next day, Defense Secretary Caspar W. Weinberger called it the latest "threat" by Brezhnev, in which he said the Soviet leader committed his nation to "an even more intensified quest for military superiority."

The Brezhnev speech provides almost a classic example of how western officials and analysts, with differing predilections or objectives, can give totally conflicting interpretations of the same event. In this case, Tuesday's elections supplied the administration with an additional political incentive to portray Brezhnev's remarks as a new Kremlin challenge.

To some government analysts who cannot be quoted by name, Brezhnev was "throwing down the gauntlet" to the United States in his address to the entire Soviet military command and in the presence of Politburo members who included Brezhnev's most likely successors.

To other analysts, Brezhnev was "picking up the gauntlet" cast by the administration's military buildup.

To still other U.S. specialists, Brezhnev was doing neither of these things. Rather, as one veteran Soviet watcher put it, Brezhnev was saying essentially that the Soviet Union would "tough it out with the Reagan administration," even though the drain on its resources would be a far greater burden than on the United States.

Brezhnev's speech and another Friday by his closest adviser, Konstantin Chernenko, clearly showed a more bristling propaganda line against the administration, intensifying the Kremlin's theme of an "American threat" to peace.

In Weinberger's words, Brezhnev was committing the Soviet Union "to a new military technology race." But privately, many administration officials said the Soviet Union is justifiably fearful of falling behind the United States in the technological race and is in a bind over the drain on its resources.

Brezhnev's speech was a message of "reassurance" for the Soviet military, U.S. sources agree. It may well foreshadow some increase in the Soviet military budget, customary each year, many U.S. analysts say, but not of the magnitude sought by Soviet military leaders.

Who is the challenger? The Soviet Union sees itself as the most vulnerable party, many U.S. specialists in and out of the government agree.

Brezhnev, as one U.S. specialist noted, by no means was making an open-ended commitment to his military, for he did not "clearly say that there is going to be an increase in anything." His emphasis instead was on the adequacy of what is already being provided to Soviet armed forces, at a time of heavy strain in the Soviet economy.

Brezhnev told his military leaders:

"We equip the armed forces with most advanced weapons and military hardware. The party Central Committee adopts measures to meet all your needs. And the armed forces should always be worthy of this concern."

Moreover, he pointedly cited "difficulties and shortcomings" in the Soviet economy, precisely in areas where consumer and military demands compete, saying, "Metal, fuel and transport continue to be the bottlenecks." He also reminded the military commanders of painful agricultural deficiencies which require "grain purchases abroad . . . ."

This is a gripping dilemma for the Soviet Union, many specialists in and out of the government agree. But only the non-governmental specialists are in position to describe it publicly.

Soviet military leaders are apprehensive about "being cut" in their share of Soviet resources, said Seweryn Bialer of Columbia University, and the Soviet leadership in turn, is "worried about Reaganism."

The concern, Bialer said, is not so much over the current U.S. military budget, "but the trend" -- concern that the present pattern will persist, with future administrations compelling the Soviet Union to compete in "tremendous military costs."

To that extent the Soviets "are afraid that our policy is working," Bialer said.

For a year there has been "a lot of muttering" in the Soviet military, said William G. Hyland, a senior Soviet specialist in the Nixon and Ford administrations. Brezhnev, Hyland said, was telling his military leaders, "Yes, the situation is getting worse, and you will get your due. But you will not get nearly what you want."

It is significant, Hyland said, that Brezhnev also cited the latest Soviet attempt to reach out to China as a potential counterweight to the United States.

Zbigniew Brzezinski, national security adviser to President Carter, said "I see the Brezhnev speech as a rather serious symptom of the simultaneous deterioration of American-Soviet and American-Chinese relationships."