When the Chernobyl nuclear power station exploded 25 years ago, authorities encased the damaged reactor in a massive stone coffin to halt the release of further radiation.
But the concrete and steel stucture, known as a sarcophagus, is so badly damaged that officials want to build a new hi-tech seal.
Two French companies, Vinci and Bouygues, were granted the contract in 2007.
Work began last year and it is expected to be completed in 2015, three years behind schedule.
The shelter will take the form of a giant arch, measuring 108 meters high, 162 meters long and 257 meters wide.
There are two layers of metal and composite materials, separated by a cushion of air.
It will be built alongside the ruined reactor and will weigh some 23,000 tonnes once complete.
However, the problem of waste disposal is yet to be solved.
France’s Areva had started on a project to build safe storage facilities for spent nuclear fuel but it pulled out in 2007.