The wife of the demolition site worker crushed by an excavator bucket in south-west Sydney has not yet given birth, the construction union says.

The 34-year-old man from Merrylands West - who suffered fatal head and chest injuries after the incident on Monday - was due to become a father yesterday or today.

A spokeswoman for the CFMEU (Construction, Forestry, Mining and Energy Union) said the baby has not been delivered yet.

The accident, at a Housing NSW demolition site on Riverside Drive in Airds, occurred when a bucket came off a 20-tonne single-arm excavator, hit a tip truck and fell on top of the man.

Police and WorkCover are investigating and a report was being prepared for the Coroner.

The demolition site is part of the area set to be redeveloped under the Airds-Bradbury Renewal Project - described as the biggest public-private partnership involving social housing in NSW.