Malaysia Airlines Flight 17 was flying from Amsterdam to Kuala Lumpur when it was hit by a surface-to-air missile on July 17, 2014, at the height of fighting in the Ukraine conflict.
The lawyer for the families, Thomas Philip, says Malaysia Airlines was negligent for failing to conduct an adequate risk assessment and for charting a course which flew through a known conflict zone, posing an unreasonable risk to those on board.
He said that the families contend the airline was in breach of contract for failing to ensure the safety and wellbeing of the flight crew.
“They failed to fulfil these duties, resulting in catastrophic loss of life,” said Mr Philip.
The families are seeking general damages for loss of support and services, damages for pain, suffering, and stress, among others, he added.
One of the relatives, Chong Seng See, said his sister — flight stewardess Chong Yee Pheng — worked for the airline for more than 18 years.
“The families of all the victims of MH17 deserve to be treated with humanity, compassion and respect. I hope [the airline] will do right by them,” he said in a statement.
A Dutch investigation determined last year that the aircraft was shot down by a Russian-made missile fired from pro-Russia rebel territory, but did not say who fired it.
Families of seven passengers from Australia, New Zealand, and Malaysia sued Russia and its president, Vladimir Putin, last month over their alleged involvement in the incident.
They filed the lawsuits in the European Court of Human Rights seeking damages of $10m (€8.9m) per passenger.
Meanwhile, a decision on how airlines should track planes in distress could be made by the end of the year, aviation trade body the International Air Transport Association has announced.
Aircraft that enter service from January 2021 must be equipped with a way of quickly recovering flight recorder data.
The importance of this was demonstrated by the loss of Malaysia Airlines flight MH370 over the Indian Ocean with 239 people on board in March 2014.
Its main wreckage and black boxes have still not been found.
The flight recorders of the EgyptAir plane which crashed on May 19 have also not been recovered, although French investigators said signals have been detected from one of them.