The incidents - one in Liverpool in June and one on the River Thames in London in September - resulted in passengers, including small children, going into the water.
"It was extremely fortunate that, on both occasions, there were no serious injuries or loss of life," said the Marine Accident Investigation Branch (MAIB) which reported on both accidents in one document yesterday.
The MAIB recommends that the vessels not be permitted to operate until the problem is sorted out.
Chief Marine Accident Inspector Captain Steve Clinch said: "The sinking of Wacker Quacker 1 in Salthouse Dock, Liverpool, and the fire on board Cleopatra on the River Thames were serious marine accidents involving WW2 DUKW amphibious vehicles."
He went on: "Although one accident involved the sinking of a DUKW as a result of flooding, and the other involved a fire, the link between both events is the foam.
"In the case of the Liverpool sinking, insufficient foam had been inserted into the DUKW; the accident on the Thames was caused by the foam being packed too tightly around machinery."
The Liverpool incident on June 15 resulted in 31 passengers and two crewmen going into the water.
The Thames incident on September 29 involved the vessel's master beaching the vehicle before ordering the evacuation of passengers and crew.