The formation of gas-filled bubbles on the surface of van der Waals crystals provides an ideal platform whereby the interplay of the elastic parameters and interlayer forces can be suitably investigated. Here, we combine experimental and numerical efforts to study the morphology of the bubbles at equilibrium and highlight unexpected behaviors that contrast with the common assumptions. We exploit such observations to develop an accurate analytical model to describe the shape and strain of the bubbles and exploit it to measure the adhesion energy between a variety of van der Waals crystals, showing sizable material-dependent trends.