Commercial production of synthetic resin has begun at the beginning of the XX century. In 1950s in the USA, small-span dome roofs, scanner assemblies and spherical hangars for radars made of plastic began to appear. Later, invention of reinforced plastics gave a possibility to use them in thin-walled shells for civil and industrial buildings. The subject of the paper associates with today’s renewed interest in thin shells. The modern theoretical base of strength analyses of composite structures give a possibility to design different structures and buildings. The possibility of the application of composites as the basic elements of thin-walled shell structures of industrial and civil purpose are illustrated by the concrete examples. The paper presents information on the well-known composite shells of positive Gaussian curvature in the form of spherical and umbrella domes or with more complex middle surfaces and presents materials that are absent in other publications. The paper contains 9 figures and 15 references. © 2017 Trans Tech Publications, Switzerland.