Shape-morphing structures are at the core of future applications in aeronautics 1 , minimally invasive surgery 2 , tissue engineering 3 or smart materials 4. Current engineering technologies, based on inhomogeneous actuation across the thickness of slender structures, are however intrinsically limited to one-directional bending 5. Here, we describe a strategy where mesostructured elastomer plates undergo fast, controllable and complex shape transformations under applied pressure. Similarly to pioneering techniques based on soft hydro-gel swelling 6-10 , these pneumatic shape morphing elastomers, termed here as baromorphs, are inspired by the morphogenesis of biological structures 11-15. Geometric restrictions are overcome by controlling precisely the local growth rate and direction through a specific network of airways embedded inside the rubber plate. We show how arbitrary 3D shapes can be programmed using an analytic theoretical model, propose a direct geometric solution to the inverse problem and illustrate the versatility of the technique with a collection of configurations.