Firefighters using hydraulic cutting gear had to free one of the men from one of the vehicles involved in the crash which occurred at just after 7.30am on Broad Road in Limavady. (Limavady Bypass).
All three were taken to hospital by ambulance for treatment to injuries which are not thought to be life-threatening.
The PSNI’s Collision Investigation Unit is now examining the crash scene.
Any witnesses can contact them on 101.