In this paper, analytical and computational solutions for stress-strain state direct problems and inverse problems of composite constructions rational design are presented. The influence of structural and mechanical properties of composite materials on the stress-strain state of parabolic antennas and reinforced domes exposed to their own weight, wind loads, and temperature is investigated, and their initial failure loads are estimated. Also, analytical solutions for inverse problems of rational design of momentless rotation shells with two families of isotensoid reinforcement structure under constant internal pressure are found. This research demonstrates efficiency and manifold possibilities for practical implementation of composite constructions with rational design methodology for reinforcement parameters.