The applications of modern fibrous reinforced composites in buildings usually must exploit unique characteristics which the materials possess: optical translucency, formability, corrosion resistance, radar transparency, light weight and ease of maintenance. Otherwise, economic factors constrain their use simply as replacements for conventional structural materials, unless the structure is mobile and weight savings are important. The widest structural use has occurred in chemical plant buildings, as pipes, tanks, vats, tubes and shrouds, where corrosion resistance is needed. Second most important is ground radome use. In both, special design criteria are imposed by certain characteristics of the material: long-time stresses must be kept to a small fraction of laboratory test strength values, and mechanical and thermal fatigue limits are very low. Both constraints derive from locally high internal stresses within the composite which promote resin matrix fractures, and eventual disintegration of the material. Recent developments suggest this can be remedied, using the same principles which operate in high impact polystyrene.