The accident happened at around 10.30am on Wednesday, June 27 at the junction of Rigg Lane at Wyresdale Road.
Police say that both drivers suffered minor injuries.
Two ambulances were sent to the scene where two women were taken to hospital by ambulance.
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A spokesman for Lancashire Road Police said in a post to Twitter: "Two vehicle collision on the crossroads of Rigg lane and Wyresdale Road Lancaster.
"Minor injury to both drivers."