While the magnitude of Venezuela's greatest natural disaster of modern times had not yet become clear last Sunday, Foreign Minister Jose Vicente Rangel estimated that at least 5,000 people had died in torrential flooding and mudslides across the nation's northern coast. The next day, he declared the death toll "definitely . . . will not be less than 10,000" and could reach 20,000. Other government officials said subsequently that the catastrophe had claimed as many as 30,000 lives.

As Venezuela struggles to cope with the calamity, authorities have conceded that the number of people who perished will never be precisely determined and that the wide range of estimates amount to guesses based on anecdotal evidence provided by survivors, visual assessments of devastated areas and census information that is outdated and incomplete.

President Hugo Chavez, who throughout the crisis has sought to allay public fears and instill hope, has offered no specific death estimates, providing numbers only of bodies recovered. But government officials say he has delegated others in his administration to do so, mindful of the fact that crucial foreign assistance depends on the extent of the catastrophe.

But what has frustrated initial efforts to estimate a death toll with even a modicum of accuracy is the fact that most victims are believed to have been buried under mud, rock and other debris unleashed by the relentless rains of Dec. 15 and 16. Vast numbers of other people are thought to have been washed away, some into the Caribbean Sea, by flood waters that engulfed entire communities.

"The topography has changed in various parts of the country; mud has totally encased some sections, and water has completely covered other places," Mario Villarroel, president of the Venezuelan Red Cross, said today in an interview. "The overall affected area is enormous, and it has been impossible . . . to get to some of the zones . . . and obtain any kind of real figure of the number of dead."

Army Gen. Manuel Salvador said: "One of the only real methods we have in trying to figure out the extent of the dead is to survey families, but even then we only get a very partial picture. All the numbers that have been put out are speculation."

The Venezuelan Red Cross, along with 75 relief workers and disaster experts from the United States and 22 other nations, is trying to arrive at a more accurate death toll, as well as one for the number of people displaced by the disaster. The government has said that about 140,000 people were left homeless, but Red Cross officials here say they believe the figure is significantly higher.

But the vast extent of destruction will not be the only challenge that relief groups and the government will face in trying to gauge more precisely how many people died. Even obtaining a rough estimate of populations in communities throughout the coastal region will be difficult, given that the last Venezuelan census was conducted in 1991.

Since then, segments of the country's underclass--which makes up the overwhelming majority of Venezuela's 23 million inhabitants--had continued to move to urban areas along the northern coast, many of them to sprawling shantytowns that have checkered the slopes of the Avila mountain range for several decades.

These hovels, many of which were obliterated by the flooding, sprouted up in the 1960s as poor, rural Venezuelans and others from neighboring countries moved to the capital region and other metropolitan areas in search of better lives. Randomly, they claimed plots of land and erected flimsy homes with virtually no interference from Venezuelan leaders of the day, who were not only overwhelmed by the influx but mindful of the potential votes these people represented.

"No one really knows how many people live in these areas, and nobody knows with any kind of precision how many people died in these areas," said Pedro Zuccarini, director of disaster relief for the Venezuelan Red Cross.

Many poor Venezuelans, emboldened by Chavez's 11-month-old populist presidency, also have invaded public and private property to build new homes, thus clouding further official awareness of how populations in many regions are distributed.