People hunt through rubble in Payakumbuh, west Sumatra
Patients flee tremor
The 6.3 magnitude quake struck close to the city of Padang in the west of the island, at 1049 local time (0349 GMT).
Rescue teams are trying to reach survivors but communications and electricity supplies have been cut.
As night fell, many people around Padang remained out in the open, too afraid or unable to return home.
The quake and a powerful aftershock had caused panic among residents on Tuesday morning, bringing many rushing out of their homes and offices.
It was like the being in a ship where you were swayed around when there were big waves
Solok resident
Eyewitness accounts
Rescue workers said hundreds of buildings had been brought down, although the BBC's Lucy Williamson in Jakarta says many of these are likely to be small, wooden houses.
Residents of some coastal areas fled to higher ground, but local officials said there was no risk of a tsunami as the earthquake happened under land rather than under the sea.
Communications cut
The epicentre of the quake was about 50km (30 miles) north-east of Padang, the capital of West Sumatra.
RECENT INDONESIAN QUAKES 6 March 2007: Magnitude 6.3 quake hits Sumatra, at least 70 dead 18 December 2006: Mag 5.7 quake hits Sumatra, seven dead 17 July 2006: Tsunami from Mag 7.7 quake off Java kills 500 27 May 2006: Mag 6.2 quake near Yogyakarta kills 5,000 26 December 2004: Tsunami from Mag 9.1 quake kills 130,000 in Sumatra
Officials said 18 people had been killed in the town of Solok, while 16 were killed in Tanah Datar.
The mayor of Solok, Samsurahim, said he could not say how many people were still trapped in the rubble.
Local hospitals struggled to cope and medical teams hastily erected tents to treat many of the wounded outside.
Christelle Chapoy, from the aid charity Oxfam's earthquake response team, told the BBC her organisation was ready to assist.
"We have a standby emergency response team based in Yogyakarta [on Java], and they're collecting information from our local partners at this stage," she said from Banda Aceh in northern Sumatra.
Ring of fire
The quake was also felt hundreds of kilometres away in parts of Malaysia, and several tall buildings in Singapore's business district swayed slightly.
Indonesia sits on the seismically active Pacific Ring of Fire, and experiences frequent earthquakes - as well as tsunamis triggered by underwater earthquakes.
Last year, more than 500 people died when a tsunami hit an area of the Java coast after an undersea earthquake.
And in the Asian tsunami of December 2004, more than 130,000 people died in Sumatra when waves destroyed swathes of the province of Aceh.
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Sumatra, Indonesia
Two earthquakes, measuring 6.3 and 6.0 on the Richter scale struck the Indonesian island of Sumatra within the space of two hours, killing at-least 70 people. The death toll may rise as a large number of buildings were destroyed and the search for survivors continues.

No tsunami warning was issued, although some people in coastal areas moved inland.  However, as the quake was under land there was no likelihood of a tsunami.

The tremors were felt in Singapore and Malaysia as well.