Modern polymer composite materials with high specific characteristics of strength and stiffness allow creating strong, durable and geometrically stable space structures. To expand the scope of application of composite materials and increase the competitiveness of space structures, it is necessary to further improve design methods with the widespread use of multiscale computational modeling of deformation and fracture processes. The paper presents the results of analysis on the strength and dimensional stability of structures made of polymer composites. A metal-composite high-pressure tank for electric propulsion systems and the design of precision reflectors for space- and ground-based antennas are considered. The methods and results of experimental and computational studies on the stress-strain and ultimate states of structures are described. The methods and means of non-destructive testing, the results of the analysis on the stress-strain state and full-scale tests of the tank structure are described. Generalized estimates of the load-carrying capacity of reflector structures under given operating conditions are given.