Currently, many studies are devoted to the use of polymer composite materials to increase the strength and stability of concrete elements. In compressed reinforced concrete elements, the bearing capacity depends on the eccentricity of the external application of the external force and the corresponding stress-strain state, as well as the location and number of composite materials glued to the surface of the structure. The choice of a scheme for placing composite materials depending on the stress state of the structure is an urgent scientific problem. At the same time, the issue of central compression and the compression of columns with large eccentricities has been well studied. However, studies conducted in the range of average eccentricities often have conflicting results, which is the problem area of this study. The primary aim of this study was to increase the strength and stiffness of compressed reinforced concrete elements reinforced with composite materials, as well as a comparative analysis of the bearing capacity of ten different combinations of external longitudinal, transverse, and combined reinforcement. The results of testing 16 compressed columns under the action of various eccentricities of external load application (e0/h = 0; 0.16; 0.32) are presented. It is shown that the use of composite materials in strengthening structures increases the bearing capacity up to 41%, and the stiffness of the sections increases up to 30%. Based on the results of the study, recommendations are proposed for improving the calculation method for inflexible columns reinforced in the transverse direction, which take the work of concrete under the conditions of a three-dimensional stress state into consideration.