Survivors of the tragedy are also taking legal action.
They are seeking punitive damages from the building's owners and those involved in its construction and maintenance.
Five Irish students and one American died in the collapse on 16 June.
The six who died were 21-year-old Irish students Eoghan Culligan, Eimear Walsh, Niccolai Schuster, Olivia Burke, LorcÃ¡n Miller - and Ashley Donohoe, a 22-year-old Irish-American.
Two law firms acting for the seven young people injured, and the parents of the six who were killed, all filed documents to the Superior Court of California in Alameda County on Thursday.
They are claiming the companies "cut corners" and had ignored "red flag warnings" that the balcony was unsafe.
Walkup, Melodia, Kelly, & Schoenberger, is representing 12 of the families.
The California-based parents of Ashley Donohoe, who are represented by Rains Lucia Stern, said that their clients were suing the companies involved in the hope that it would "bring to light the negligence and carelessness that caused this entirely avoidable tragedy", one that produced "so much pain and loss" both in the US and in Ireland.
In the legal papers filed, seen by RTÃ‰ News, the families said they also want to "hold accountable" those responsible for the deaths and injuries, and to highlight their behaviour "so that a similar tragedy never occurs again".
Thirteen young people who were celebrating the 21st birthday of one of the injured, Aoife Beary, were standing on the balcony when it gave way.
Wooden beams supporting the balcony had been badly rotted by water damage, the Berkeley Building and Safety Division confirmed.
The facts of the case will be decided under California law and the amount of any damages will be decided by a jury
The parents of six students killed in a balcony collpase in Berkeley, California, have begun legal proceedings against more than 30 firms involved with the apartment complex.