Travelers arriving on the overnight train from Kiev this morning all had heard about the accident back in Chernobyl but showed no particular alarm as they discussed it in the busy Kiev station here.

"Oh, yes, I heard about it," said one woman, weighed down with suitcases and parcels. "They talked about it on the radio. But, you see, I live in Kiev [60 miles from Chernobyl] and there, everything is normal."

Privately, however, several Soviets said the subject was on everyone's mind today. "It is a very frightening thing," said a 76-year-old woman. "There is no knowing where it will lead, maybe hundreds or thousands will die later."

Still, judging from many people's comments, it seemed that the prospect of uncontrolled radiation has not set off the kind of widespread public fear that it might elsewhere. As one diplomat noted, public consciousness here about the dangers of nuclear radiation is not what it is in the West.

Like other news items here, the one about Chernobyl has had to be weighed and balanced by attentive listeners. On tonight's evening news, both the newscaster and the commentator referred to exaggerated western accounts on casualties and damages at the power plant.

Many Soviet listeners are prepared to believe that the western media are using the incident to embarrass their country. But at the same time, many are also prepared to believe that there is more to the story than is announced on the news program.

"Of course, there is more," said one middle-aged Muscovite. "Just the way they are reading it on television tells you that."

At the Kiev station this morning, one woman was walking ahead of her husand when she stopped to answer a reporter's question. "It was on television and they said . . . ," she said, but before she could finish her sentence, her husband interrupted.

"They said two people died. That's all. The others are working," he said firmly and hustled his wife off.

As streams of Moscow commuters poured off the "elektrichki," or suburban trains, a porter paused before answering. "Accident?" he said. "You mean the one about a week ago?"

The second-day announcement about the Chernobyl accident had listed two people dead and four towns evacuated, so people knew something serious had happened, but they were not sure what. That made Soviet public reaction, which is virtually impossible to measure, particularly elusive today.

People who were asked for reaction on the street showed a vagueness bordering on indifference that contrasted sharply with the public alarm raised all over the United States during the accident at Three Mile Island in 1979.

So, while the rest of world is riveted and alarmed by the events in Chernobyl, Moscow goes along, on the surface, as if nothing extraordinary were going on.

Spring weather has finally arrived, leaves are green at last and the city is decked out for Thursday's May 1 holiday. Tonight, the first item on the news was a sentimental account of how the country's three biggest cities -- Moscow, Leningrad and Kiev -- are preparing for the occasion.

As western experts debated long-term contamination of Kiev's drinking supply, Soviet television was showing pictures of tulips and fountains in the city's main square.

Later, a commentator reported that the quality of drinking water and water in rivers was in keeping with normal standards.

In the absence of any independent information, both foreigners and Soviets are at a loss to judge the severity of the accident. "Nobody knows anything. What do you think? It only happened a day ago," said a 32-year-old man.

But the rumors have started -- in Kiev, where people have heard figures on casualties ranging from 300 to 3,000, and in Moscow, where someone reported hearing that several hundred injured had arrived here for treatment.

In Western Europe or the United States, such reports would not be worth repeating if they could not be officially confirmed. But here, telephone inquiries to the area -- to Kiev, Chernobyl and Pripyat, another town in the vicinity -- have been met by such answers as, "I am not authorized to give that information," or "I have no information," or the bolder, "Everything here is normal."

Sometimes even the appearance of normalcy is sufficient. In today's edition of the communist newspaper Pravda, there were seven pictures taken in the Ukraine, showing people in national costumes, dancing and getting ready for May Day. On page 2, at the bottom, was a small article titled, "From the Council of Ministers," giving the official statement on the accident.