A new type of adaptive structure is presented that relies on a pressure derential to perform gross structural deformations. This structure relies on highly compliant honey-comb cells that can be pressurized externally or can rely on a pressure differential that exists at elevated altitudes. By pressurizing this honeycomb, its stiffness can be altered and deformations can be controlled by means of a restoring force. The mechanics of this pressure-adaptive honeycomb is laid out in this paper. The concept of equivalent material stiffness is introduced that assigns a Young's modulus to the honeycomb wall material that includes both the material-induced stiffness and the pressure-induced stiffness for a given cell differential pressure. The application of this model in a finite element analysis of a beam specimen is shown to correlate well to experimental results. In addition, the paper discusses possible applications for pressure adaptive honeycomb such as a Gurney flap and a solid-state flap. Wind tunnel test on a test article of a wing with pressure-adaptive flap demonstrates an increase in lift coefficient of 0.3 over a wide range of angles of attack. By increasing the pressure inside the flap to 40kPa its equivalent stiffness increases from 15kPa to 109kPa, thereby allowing the camber to decrease from 7.2% in deployed position to 2% in stowed position and shifting the point of maximum camber from 72% of the wing chord to 40%.