This article considers the prospects of the application of building structures made of polymer concrete composites on the basis of strength analysis. The issues of application and structure of polymer-concrete mixtures are considered. Features of the stress-strain state of normal sections of polymer concrete beams are revealed. The dependence between the stresses and relative deformations of rubber polymer concretes and beams containing reinforcement frame and fiber reinforcement has been determined. The main direction of the study was the choice of ways to increase the strength characteristics of concrete with the addition of a polymer base and to increase the reliability of structures in general. The paper presents the results of experimental and mathematical studies of the stress-strain state and strength, as well as deflections of reinforced rubber-polymer beams. The peculiarities of fracture of reinforced rubber-polymer beams along their sections have been revealed according to the results of the experiment. The peculiarities of fracture formation of reinforced rubber-polymer beams have also been revealed. The conducted work has shown that the share of longitudinal reinforcement and the height of the fibrous reinforcement zone are the main factors. These reasons determine the characteristics of the strength of the beams and their resistance to destructive influences. The importance and scientific novelty of the work are the identified features of the stress-strain state of normal sections of rubber-concrete beams, namely, it has been established that the ultimate strength in axial compression and tension, deformations corresponding to the ultimate strength for rubber concrete exceed similar parameters for cement concrete 2.5–6.5 times. In the case of the addition of fiber reinforcement, this increase becomes, respectively, 3.0–7.5 times.