In the paper, mathematical modeling methods for describing the behavior of sandwich panels with a tetrahedral core under various loads have been used, and a series of numerical calculations carrying out by the ANSYS software. In so doing the previously obtained effective elastic characteristics were taken, which made it possible to replace the direct modeling of the tetrahedral core structure with elements of a simple form using orthotropic material with equivalent characteristics. The problem of the plate’s three-point bending was solved, and a deformed state and deflection character of the panel were analyzed. The necessity of applying the heteromodular elasticity theory when modeling such objects and of taking into account the effective elastic characteristics obtained by tension and compression of the periodicity cell was established. Recommendations were given for the use of periodicity cells when computing the iterative changes in material properties and effective characteristics obtained during tension and compression.