The unit on Enterprise Park, a small industrial estate on Beck View Road, was broken into for the second time in a month at around 1.30am yesterday.
A Humberside Police spokesperson said: "Intruders entered the premises causing damage to windows and doors as they attempted to steal the company safe.
"Police attended and gave chase to the offenders who escaped from the scene on an off-road motorbike. The pursuit continued through into Hull where the offenders then left the road and went across country to evade capture."
Officers have appealed for information about the culprits and asked people to call the non-emergency number 101, quoting log 24 of July 25.