Bodies were recovered from the wreckage last night and taken for post-mortem examinations to the Midland Regional Hospital in Tullamore.
The aircraft had taken off from Clonbullogue airfield at around 2.25pm. The crash happened a few miles away in bog land near Edenderry.
The Clonbullogue facility is popular with skydivers.
A Garda spokesman said there were 16 parachutists on board.
"All 16 made their jump from the craft," he said.
"However, witnesses then saw the aircraft crash shortly afterwards. There were two people on board, the pilot and a seven-year-old boy."
Local councillor Eddie Fitzpatrick said the airfield had a long established reputation for parachuting.
"People would be over there all the time, especially at weekends in the summer, a lot of people parachuting and a lot of fundraising jumpers," he said.
"It's a great shock to hear of an accident like that happening."
Fellow Offaly councillor Noel Cribbin said: "This is a big shock to the area.
"These flights have been happening for the last 20 years and this is the first time I've heard of a plane going down."
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