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