The use of nonmetallic reinforcement in concrete aims at the decrease in material consumption by reducing the component sizes when compared to conventional reinforced concrete structures, which inherently results in very filigree structures. Although intensive basic research has been carried out on textile-reinforced concrete for about 30 years, the subject of stability behavior has hardly been investigated so far. This study focuses the fundamental understanding of the structural behavior of slender carbon-reinforced concrete (CRC) structures subjected to axial compression. Therefore, buckling experiments have been carried out in order to quantify the influence of two parameters: the slenderness ratio of the specimens (varying between 60 and 130) and the load eccentricity (0, 2, and 4 mm). The results of the specimens that were tested with the initial load eccentricities revealed a good overall agreement with those obtained by a second-order theory approach throughout all of the investigated slenderness ratios. For the centrally pressed samples that featured high slenderness ratios, the failure stresses could successfully be predicted with Euler’s buckling formula, whereas this theory overestimated the results of the specimens with intermediate to low slenderness ratios due to the plastic buckling phenomenon. The presented study emphasizes that the consideration of the stability problem is inevitable when designing material-efficient structures made of textile-reinforced concrete.