Underground hydrogen storage chambers

can be constructed using

Blind Bore Shaft Drilling commonly used in mining

Sequence of photos of mine shaft construction 
Courtesy of Abergeldie Complex Infrastructure (Australia - www.abergeldie.com

Drill site ready for shaft construction
Drill head assembly 
Drilling initiated
Shaft liner installation
Completed shaft with liner
Shafts up to 6.5 m (21 ft) in diameter