Carbon neutrality demands adoption of alternative construction strategies, departing from the widely used steel-reinforced concrete. Carbon reinforced concrete offers the possibility to build segmented slabs with very thin webs and flanges, therefore reducing the material consumption. However, thinner structural members are susceptible to buckling. The present paper presents six small scale series of compression test. Specimens with a thickness of less than 28 mm are reinforced with different textile carbon reinforcement grids. Two subgroups of manually produced carbon grid reinforcement, one with a novel diagonal branching and merging yarn path, and the other with yarns perpendicular to each other, show significant difference in the stress-strain behaviour. The behavior is non-linear for the first and linear for the second mentioned. In addition, industrial produced biaxial Q85 carbon textile was investigated with warp or weft direction under compression. No influence in the stress-strain behavior was observed. The ultimate stress of the specimens with diagonal reinforcement is 13% and with yarns perpendicular to each other 9% lower than for the biaxial Q85 reinforcement. The results of this study provide a solid foundation for future large-scale investigations.