The smash between the two HGVs happened at around 9pm on the A41 at Tern Hill.
One of the men had to be helped from his vehicle by firefighters, while the other man was able to free himself. Both were taken to hospital via ambulance.
Four fire engines were sent to the scene and police were in attendance.
Mobilised 21:03 Thursday with @FireHodnet #Loggerheads @StaffsFire @SFRS_Wellington and @SFRS_JimBarker 🚒🚗 to RTC 2x LGV tankers at #A41 #StokeHeath 🚚💥🚛 1x Adult male assisted from vehicle 👩🏻🚒👨🏻🚒 2 x casualties to hospital via @OFFICIALWMAS 🤕🚑 @OPUShropshire @MDraytonCops 🚓 pic.twitter.com/PqDLqTn0SZ— Market Drayton (@SFRS_MDrayton) March 26, 2021
A Shropshire Fire & Rescue spokesman said: "At 9.03pm we received a call reporting that a road traffic collision had taken place in Tern Hill.
"Four fire appliances were mobilised from Hodnet, Market Drayton and Wellington. An operations officer was in attendance.
"Road traffic collision involving two large goods vehicles - one person extricated by fire service personnel, one person self extricated, diesel spillage contained by fire service."