Important characteristics for temporary structures include ease of deployment, simple erection, and minimal shipping volume and weight. The use of inflatable fabric members (i.e. airbeams) directly satisfies these needs due to their light weight, small packed volume and simple inflation. The focus of this study is the bending response of inflatable, braided beams and arches with external reinforcing straps, which are currently used as main load-carrying members in rapidly deployable military tents. Of primary interest was experimentally determining the constitutive properties of the constituent materials, and quantifying the load-deformation response of beams and arches with full-scale laboratory tests. The straps were tested in pure tension to obtain an accurate tensile modulus. The braided material was tested in torsion to obtain shear modulus as a function of inflation pressure. A beam finite-element model that accounts for braid angle and strap stiffness was developed to model the bending response of the inflatable, braided, strapped beams and arches. Quasi-static load-deformation tests of arches and beams were performed to provide data for model validation. The FE model effectively predicted the load-deformation response of the members to and beyond the point of fabric wrinkling.