One theory is that the works were stolen to order for a private collector and have been taken to eastern Europe.
Masked raiders snatched a self-portrait by the Dutch master, Rembrandt, and two works by the French impressionist Renoir - together worth an estimated $30m - before escaping by boat.
One theory is that the works were stolen to order for a private collector and have been taken to eastern Europe.
Sweden has asked Interpol to join the search for the suspects, and police forensic scientists have been combing the museum for clues.
The three thieves walked into the museum in central Stockholm at about 1715 (1615 GMT), as it was preparing to close for the day.
One, armed with a machine gun, held up security staff while the other two ran to different rooms upstairs
After ordering guards there at gunpoint onto the ground, the two thieves went straight for their target paintings. Within moments all three had left the building and sped off into the darkness on a small motor boat waiting for them near the museum.
They spread nails in front of the museum before they fled, police said.
Other people are also thought to have been involved in the crime, as two phone calls reported car fires in the area at the same time that the gallery alarm went off at police headquarters.
The subsequent confusion apparently gave the robbers the time they needed to escape.
About two hours after the theft, investigators recovered the getaway boat on the banks of the Malar lake in southern Stockholm.
It was taken to a laboratory to be checked for fingerprints and other clues.
But there is, as yet, no lead on the suspects, said Police Inspector Thomas Johansson.
"We're still looking for them, they could escape quite easily," he told the French AFP news agency. "There's no ice on the water at the moment, it's open water and it's dark."
The works stolen were: Self Portrait by Rembrandt, and two paintings by Renoir - Conversation with the Gardener and Jeune Parisienne. They were each valued at between $7.5m and $10m (75 million and 100 million Swedish kronor).
None of the paintings were insured.
'Contract job'
Inspector Johansson said the thieves could have disappeared on to any of thousands of tiny islands in the archipelago off Stockholm, or into the dense forests that surround the city.
"This was professional work," he said. "It looks like a case where someone ordered them to steal the paintings - a contract job.
"It's not going to be easy to sell these paintings on the open market, so it must have been someone who just wanted the paintings for their own sake."
The theft is the biggest in Sweden since robbers cut through the roof of Stockholm's Modern Museum in 1993 and stole eight works of art by cubist masters Pablo Picasso and Georges Braque worth about $60m. Most of the works were later recovered.