Officers were called to the A59, close to the Samlesbury Hotel, at around 3.30pm after a man called 999 and said a black Audi A3 had hit his vehicle.
The car was pulled over before the men, described as white and in their early 20s, got out and fled through nearby bushes and into the field, the man told the operator.
The search was still ongoing at around 5pm, with dog units called to the scene to help.
Meanwhile, officers used social media to urge the public to report any sightings of men - two in light coloured t-shirts - in the area.
A spokesman for Lancashire Police said nobody is understood to have been injured in the crash. He was unable to give details of the other car.