Emergency services were called to the collision in Bostal Road at around 1pm.
Police said a blue Nissan sports vehicle and a large blue Dodge pick-up truck, both travelling from the direction of Steyning, were in collision with a Skoda Octavia car which had been driving from the direction of Sompting.
Another Skodia Octavia collided with the rear of the first Skoda, officers added.
Police said a 75-year-old woman, who was driving the first Skoda, and her two passengers, a 79-year-old woman and a 78-year-old man, were trapped in the vehicle.
Firefighters from Hove, Shoreham, Henfield and Worthing released all three using hydraulic rescue equipment, the fire service added.
Three ambulances, two paramedic cars and three vehicles from the Hazardous Area Response Team (HART) were sent to the crash along with an Air Ambulance.
A spokesman for South East Coast Ambulance Service (SECAmb) said one of the women was taken to the Royal Sussex County Hospital in Brighton as a priority. Her injuries are not thought to be serious.
Two others were also injured and were taken to Royal Sussex County Hospital for further treatment, the spokesman added.
The road was closed between the Clays Hill junction and the Newham Lane junction. It has since been re-opened.
After the incident police said a 19-year-old man from Storrington, who was driving the Nissan sports, and an 18-year-old man from Worthing, driving the pick-up truck, were arrested on suspicion of causing serious injury by dangerous driving. They have been released on bail until July 21 while enquiries continue.
Sergeant Neil Walker of the Surrey and Sussex Road Policing Unit said; “Anyone who saw what happened, and in particular anyone who saw the sports car and the truck leaving Steyning is asked to contact us via [email protected] or call 101 quoting Serial 672 of 03/05.”
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