The first blast went off at one of the entrances to the festival at the Tushino airfield as the Russian band Crematorium played for a crowd estimated at up to 40,000. Another went off about 10 minutes later as spectators tried to leave by another gate.
Officials said the first bomber's device did not go off completely and that the majority of the casualties were caused by the second explosion.
Moscow city police spokesman Valery Gribakin said 14 people were killed, not counting the two female bombers, who also died. He said about 60 people were wounded. NTV television and the Interfax news agency reported that two more blast victims had died in hospitals, but that could not immediately be confirmed.
Gribakin denied earlier reports of a third blast.
Guards at the festival entrances were suspicious of the women and prevented them from entering the grounds, said First Deputy Interior Minister Rashid Nurgaliyev.
"When they approached the entrance, their agitation was visible. They tried to get in too fast and were turned away," he said.
After the first bomb went off, police directed people trying to go through the nearby exit to leave through another gate - and there the second bomb was detonated, said Rustam Abdulganiyev, a 17-year-old who had been inside the airfield.
"I've never seen anything like it," he said.
Bodies lay splayed on the pavement, surrounded by pools of blood. Emergency response officers covered them with black plastic garbage bags.
Anxious relatives who had heard of the blast on Russian radio and television crowded the entrances but were barred from entering the airfield.
Manana Gogoa's son David, 14, was attending the concert with a friend. "We don't know anything. We just heard it on TV. They won't tell us anything," she said, weeping.
Many frightened parents had tried to call their children's cellular phones, but the service of one of the Russian capital's main cell phone networks wasn't working in the Tushino area.
Helicopters scoured the skies over the field, and ambulances and police trucks streamed in. Police discovered another explosive device near one of the entrances to the festival and defused it, the ITAR-Tass news agency said.
Interior Minister Boris Gryzlov said suspicions pointed to Chechen rebels. News reports said a passport found at the bombing site identified a Chechen woman.
Gribakin said 13 identification papers, including passports, train tickets and student IDs, had been found at the blast sites and most had been matched up with the dead.
Aslambek Maigov, the envoy of Chechen rebel president Aslan Maskhadov, denied that Maskhadov was connected to the bombings. But the Chechen rebels are deeply factionalized and only a small portion are believed to follow Maskhadov's direction.
Chechen rebels have shown an increased penchant for targeting civilians over the past year with suicide-bomb attacks. Fears of terrorism have been high in the Russian capital since last October's seizure of a Moscow theater by scores of Chechen militants, including women strapped with explosives and detonators.
The one-day festival, called "Krylya" (Wings), is a highly popular summer event for Moscow's youth, featuring many of the country's most renowned bands. The weather Saturday afternoon, cool and partly sunny, was ideal for attracting a large crowd.
Many in the crowd were oblivious to the blasts. While performers were informed, organizers decided not to announce the explosions or cut short the festival for fear of unleashing panic in the crowd.
"There's no reason to spoil the party and there's no need to say anything that's unconfirmed," Sergei Galanin, one of the festival's announcers, told reporters.
The attack came hours after Russian President Vladimir Putin signed an order setting presidential election in Chechnya for Oct. 5. The elections are the latest step in Putin's strategy of trying to bring a political resolution in the Caucasus republic even as fighting continues.
However, rebel attacks have undercut the Kremlin's effort to portray the situation in the war-shattered region as stabilizing.
CBS News Correspondent Richard Roth reports Russian officials claim foreign terrorists, including al Qaeda, are financing violent resistance to the political process.
In June, a female bomber blew up a bus carrying workers from a Russian air base near Chechnya, killing herself and at least 14 people.
In May, an explosives-laden woman blew herself up in the middle of a crowd of Muslim pilgrims, killing at least 15, in an apparent attempt to kill the Kremlin-backed acting president of Chechnya, Akhmad Kadyrov. Two days before that attack, three suicide bombers detonated a truck loaded with explosives outside a government compound, killing at least 59 people.
During the Moscow theater standoff in October, Chechen militants threatened to blow themselves up and held 800 people hostage for days. Russian special forces ended the standoff by pumping narcotic gas into the theater and then storming in. At least 129 hostages died, almost all from the effects of the gas.