Police and fire crews have been called to three arson attacks on a block of flats in Scunthorpe within a week.
Officers were called to Sutton House in the early hours of 3 April, then at 2200 BST the same day, and again on Friday at 0100 BST.
In each case the culprit had sent burning rubbish down the rubbish chute.
Humberside Police said the incidents were putting people's lives in danger and asked residents to be vigilant.
No-one was injured in the attacks.
Pete Baron, of Humberside Fire and Rescue Service, said: "Arson is always a real problem to us and needlessly puts lives in danger.
"This type of mindless act means that our fire engines are tied up when they should be available for other emergencies.
"People who do this should realise that the consequences could be very serious should their actions result in someone being seriously injured or even killed."