The crash happened at 2.40pm on Friday, July 2 at the Bramham Crossroads.
Three crews from Tadcaster, Wetherby and Acomb were called to the scene.
North Yorkshire Fire & Rescue confirmed that crews extricated occupants of the cars using hydraulic cutting equipment, sharps protection and casualty care equipment.
The occupants of the vehicles were then left in the hands of the paramedics on scene.
Police have been contacted for further information.