Inflatable wings are of interest for applications where low weight, compact transport volume, and easy set-up are important. Examples are unmanned aerial vehicles with inflatable wings, paragliders and softkites for sport or airborne wind-energy applications. In this paper, a new method of designing and fabricating conformable inflatable wings by Jacquard three-dimensional weaving is presented. Depending on the weaving pattern, plane-parallel, tapered, or even curved structures can be produced. An analytical framework was developed to determine the shapes of pressurized structures produced by Jacquard weaving. Based on this theory, several design patterns suitable for inflatable wings are proposed. It is shown that the structural efficiency of the woven structure is identical to the structural efficiency of a cylinder. To validate the concept, different wing prototypes were built with the methods used for the mass production of airbags. The new method allows for the cost-efficient fabrication of inflatable structures, pressure vessels, and liquid containers with applications in the automotive, aerospace, and leisure industries.