•The tensile response of Textile Reinforced Concrete can be softer compared to fabric.•The failure load of the composite may be lower with respect to the bare fabric.•Experimental observations can be justified by differential activation of filaments.•Bond lag can be implemented in a coaxial ring model for the composite.•Such approach allows calculating the cracked stiffness and failure load of the composite. Textile Reinforced Concrete (TRC) is a cementitious composite material where a carbon or glass fabric is embedded as reinforcement. The use of TRC allows building thin and light structures, with reduced concrete covers and an enhanced durability due to the absence of corrosion problems. In this article, the response of TRC elements subjected to tension is reviewed by means of an experimental and theoretical investigation. A test programme comprising 28 specimens reinforced with uncoated and coated carbon textile fabrics is presented. Detailed measurements were performed by using Digital Image Correlation allowing to investigate on the crack development and failure in tension of the specimens. On this basis, a comprehensive approach to address the tensile response of TRC is presented based on a coaxial ring model incorporating different constitutive laws for the core and sleeve filaments and their interfaces. The model is observed to consistently predict the various responses measured experimentally, both in terms of the stabilised cracking phase and failure load, avoiding the need to consider empirical efficiency factors. The results are finally compared to available tests in the scientific literature showing consistent and fine agreement.