Wold Construction managing director Ian Woolfitt was found under the truck at a haulage yard on Tuesday.
Wold Construction safety adviser Andrew Scargill told the Hull Daily Mail: “We believe he had nipped there to do a quick job.
“The Iveco tipper had a flat tyre. We think Ian had been attempting to change it.
“In order to access the spare tyre, you have to tip the trailer up using the mechanism.
“Because there were no witnesses, it is very difficult to ascertain exactly what has happened.”
Woolfitt was described as a “hands-on” boss by his colleagues.
Scargill said: “He was a managing director in overalls. You would never have found him sitting at his desk. That was not his style.”
Wold Construction has been in business since 1991 and specialises in building and civil engineering contracts up to £4.5m.
A Humberside Police spokeswoman said they received a report of a man trapped under an Iveco tipping trailer shortly before 4pm on Tuesday.
She said: “Police, fire and ambulance service attended but, sadly, the 65-year-old man was pronounced dead at the scene.
“The Health and Safety Executive was advised of the incident and attended. An investigation is now under way involving both the police and HSE.”