In one embodiment of the present invention, a stress analysis engine efficiently computes stresses for an arbitrarily shaped three-dimension (3D) model. In operation, the stress analysis engine slices the 3D model into layers of cross-sections. The stress analysis engine then groups the cross-sections into virtual cross-sections. For each virtual cross-section, the stress analysis engine applies bending moment equilibrium-based equations to determine a corresponding structural stress for the 3D model. The efficiency of this stress analysis process enables real-time feedback of stresses to an interactive design tool that facilitates a trial-and-error design process. Using this trial-and-error process reduces the guesswork and/or over-engineering associated with conventional approaches based on finite element methods that are typically too slow for interactive feedback. Consequently, the disclosed cross-sectional stress analysis techniques enable efficient design of 3D models that produce structural robust 3D objects when manufactured by a 3D printer.