An efficient method that employs the virtual equivalent projected model (VEPM) is introduced and formulated in this study to simulate local failures in face sheets and cores of sandwich plates with pyramidal truss cores. This approach is based on two-dimensional FE-analysis that uses the projected shapes of 3D pyramidal truss cores and utilizes virtual properties from the homogenized equivalent elastic-plastic properties of the original material and geometries. To establish the validity of this approach, virtual equivalent projected models are applied to three-point bending, clamped bending and U-bending analyses. The results of simulations have shown that the load-displacement curves and deformed shapes with local failures of the VEPM are analogous to 3D pyramidal cores in three types of bending processes irrespective of the materials and core geometries. In addition, the computational time was greatly reduced. The practicality of this approach has been shown through comparison with the experimental results.