Emergency services attended the incident on Mythop Road at around 4.15am this morning.
Fire services arrived to find a car "well alight" and a crashed car with an injured woman nearby.
The police helicopter was called out to assist with the search for the missing men.
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A spokesman for Lancashire Police said: "We were called out this morning when a car came off the road and hit a tree.
"It seems a car was already on fire in the road when another car came and tried to avoid a collision with the burning car. It left the road and hit a tree.
"Two male occupants ran off from the vehicle. A female occupant was found with a shoulder injury in the car and was treated by paramedics.
"We are still looking for the men and our investigations are on-going."
Crews from South Shore and Blackpool used hose reels to extinguish the blaze.
Watch Manager Kevin Warwick said: "We arrived to find a car heavily involved in fire which was extinguished using a hose reel.
"There was also an RTC where a car left the road as it tried to avoid the other burning car.
"The occupants of this car managed to get out unassisted and a girl with a shoulder injury was treated by paramedics.
"The fire is being treated as deliberate and an investigation has been launched. "
Anybody with information can contact police on 101 quoting log reference 0143 of May 17.