The family were killed when their Fiat collided with an articulated lorry on the A801 near Polmont, on the outskirts of Falkirk in Scotland, at around 2.20pm.
The mother and father were in their 20s while the children were under the age of three.
Their car had crossed into the path of oncoming traffic before the crash, police said.
The lorry driver was treated at the scene for shock.
Superintendent Iain Murray said: "This was a tragic collision which sadly killed all occupants of the car.
"We would like to hear from anyone who may have witnessed this crash, or who has information that can help, so that we can piece together the circumstances.
"We are particularly keen to trace a silver people carrier which was seen near to the site of the crash."
The crash happened near the Lathallan roundabout by junction four of the M9.
The A801 between Lathallan and Bowhouse has been closed while police investigate the cause of the accident.
A spokeswoman for the Scottish Fire and Rescue Service said: "We got a call at 2.25pm and sent appliances from Falkirk, Bo'ness and Larbert.
"We cut one person out of the car using cutting gear but there was nothing else more to do at the scene so we sent two appliances back and kept on the scene to wait for the fire accident investigation team."
Anyone with information is asked to contact Police Scotland on 101.