Casualties had to be cut free from their vehicles after a collision between a car, a minibus and lorry in Gainsborough.
Emergency services were called to Thorndike Way after reports of the collision after 3pm on Thursday, May 12.
The fire service used cutting tools to remove two casualties from the Vauxhall Zafira car and one casualty from the Ford minibus.
The male car driver and female minibus driver were taken to hospital.
A police spokesman said the injuries are not believed to be life threatening.
The force are also appealing for any witnesses who might have seen the incident to get in touch by calling them on 101, quoting incident reference number 203 of May 12, 2016.