Inflatable structures made of modern textile materials can be inflated at high pressure in order to be used as strong building elements. The aim of the paper is to present results from research on the mechanics of highly inflated structures. Experimental, analytical and numerical studies on the behavior of inflatable fabric beams are displayed. We will first describe experimental studies on two kinds of inflatable prototypes: flat panels and tubes. Experiments show that their behavior is a linear combination of yarns and beams shapes. The usual theory of collapse analysis is then applied to the computation of wrinkling loads of these fabric beams. The second section of the paper is devoted to build a new inflatable beam theory and to show that the compliance of the inflatable beams is the sum of the beam compliance and of the yarn compliance. A new inflatable beam finite element is developed in the third section and used to compute deflections of hyperstatic beams. Our first results on the buckling of inflatable panels are displayed in the last section. Comparisons between experimental and analytical results are shown and show that this new theory on the mechanical strength of inflatable structures at high pressure is satisfactory.