LONDON—Royal Dutch Shell PLC on Thursday posted a 60% drop in second-quarter profit, largely because the oil and natural-gas giant wrote down the value of its North American shale assets by more than $2 billion after tax, highlighting the difficulties that energy companies face in finding new oil they can pump at a profit.

Shares in the Anglo-Dutch oil company fell after Shell said its current cost of supplies—a figure that excludes gains or losses from inventories and is therefore equivalent to the net-profit figure reported...