The collision happened just after 7.20pm on the B1192 Langrick Road, between Langrick and New York.
Two vehicles were involved, a silver BMW 5 travelling south towards Langrick, and a silver Kia Venga travelling north towards New York.
Lincolnshire Fire & Rescue attended the scene, with crews from Boston, Kirton, Donington, and Leverton using ladders to gain access to the vehicles, and specialist cutting gear to extricate the three casualties from the cars.
Three people were taken to hospital with injuries described as serious.
Police are now appealing for anyone who was travelling on Langrick Road and saw either vehicle prior to the collision, or the collision itself, to get in touch.
A spokesman said: “We also ask for anyone who was in the area to check any dashcam or similar recording devices for any footage that may assist our investigation.
“If you can help, there are a number of ways to get in touch.”
Anyone with information can either email [email protected] or call Lincolnshire Police on 101, quoting Incident 379 of 27 March.