The recent development of construction via 3D concrete printing (3DCP) has brought the need to address new challenges when facing the structural computation. It has been reported of primary necessity to be able to accurately evaluate the buildability failure of this type of structures, which may occur due to two distinct phenomena: elastic buckling (self-buckling) or plastic flow. This study proposes a new numerical framework for the calculation of the buildability failure in 3D-printed concrete structures, combining a novel constitutive model featuring key early material behaviours, including tensile and compressive damage, irreversible strain, creep, and aging effects. To simulate the printing process, a finite element strategy based on the GCode print path read by the in-house FE code FEMUSS is adopted to realistically reproduce the deposition of concrete. This is combined with a large displacement strategy to model the phenomenon of elastic buckling. The effectiveness of the proposed model is verified via the simulation of four concrete printing experiments reported in the literature: straight wall, hollow cylindrical wall, large hollow square wall and small hollow square wall. Numerical results show that the model is able to accurately reproduce the failure mechanisms, including plastic flow and elastic buckling (self-buckling) with accuracy, as well as the structural response throughout the printing process. In addition, the model can predict the exact deposition layer in which structural failure occurs, providing valuable insights for practitioners. This study promotes the advance of 3D concrete printing by providing a powerful numerical tool to evaluate the printability and structural integrity during 3D concrete printing, allowing to optimize printing parameters and material formulations with the aim of improving the structural performance.