In this work, the lattice model is applied to study the printing process and quantify the buildability (i.e., the maximum height that can be printed) for 3D concrete printing (3DCP). The model simulates structural failure by incorporating an element birth technique, time‐dependent stiffness and strength, printing velocity, non‐uniform gravitational load, localized damage, and spatial variation of the printed object. The model can reproduce the plastic collapse failure modes reported in the literature. In this research, three main contributions for 3DCP modeling work can be found. A new failure criterion is proposed and adopted to improve the estimation of critical printing height; the element birth technique is utilized to mimic the continuous printing process and study the impact of non‐uniform gravitational load; variability of a printed structure is modeled through the inclusion of disorder during mesh generation and Gaussian distributions of material properties. Using this model, parametric analyses on non‐uniform gravitational load and material variation are conducted to assess their impact on the failure–deformation response and the critical printing height. Finally, the model is validated by comparison with two 3D printing experiments from the literature. The proposed lattice model can reproduce the correct failure‐deformation modes of two types of structures commonly used for buildability quantification: A 3D‐printed hollow cylinder and a square wall layout. Lattice modeling of the square structure yields a relative difference of around 10% with the experimental printing height. For the cylinder structure, the predicted radial deformation and corresponding height show good agreement with the experimental data; the model yields a 41.38% overprediction of the total number of printing layers, compared with the experimental data. Possible reasons for the quantitative discrepancy are discussed.