Cross was killed along with his 32-year-old wife Crystal Cross and their seven-month-old son Grayson Cross.
The soldier was based at CFB Petawawa with 2 Service Battalion, according to Capt. Jeremy Mathews, a public affairs officer at the base west of Ottawa.
Two people from Pennsylvania also died in the crash, authorities said.
Area media outlets reported that the crash occurred Saturday night in the northbound lanes of the heavily travelled interstate in Florence County. It involved five vehicles, including two tractor-trailers, and two cars that caught fire. The incident is still under investigation.
Training to be vehicle technician
Cross joined the Canadian Armed Forces almost three years ago and was training to be a vehicle technician with 2 Service Battalion, according to a statement from battalion acting commanding officer Maj. Brian Lepack.
"Although only with us for a brief time, Private Cross was a member of our military family. He was a new soldier and was just beginning to show promise in his career," Lepack wrote.
"Private Cross was well liked by his peers and the shock of his death has been felt by all who knew him," he wrote.
Lepack said the loss of the family was felt by both military and civilian personnel.
"We all share in the loss of this young man and his family and I can tell you we will do everything we can to support his family during this difficult time."
Florence County coroner Keith von Lutcken identified the Pennsylvania victims as Jacqueline McCann, 51, and Barry Himes, 52, both of Johnstown.