A truss-core sandwich panel is a promising load-bearing element of lightweight high-stiffness structures. The use of this element in load-bearing structures makes it necessary to know its mechanical and strength characteristics depending on the structure and properties of a typical core cell. Currently, the available results are not sufficient to assess the strength due to the complexity of taking into account all the features of the loading of the core structure in the form of repeated pyramidal and tetrahedral unit cells most common in the production of lightweight truss cores. In the research of the strength properties of a unit cell, it is assumed that the destruction of the truss structure may occur when the yield stress in the material of the core is exceeded or if buckling takes place. The scheme of destruction of the truss structure in the cell will depend on the combination of unit cell equivalent stress values. The critical core buckling stress is usually less than the yield stress. Therefore, when co block diagrams of equivalent stress constraints are constructed, one can observe a rather complex picture of the change in the limit values depending on the azimuthal angle in the plane of the cell base. To analyze limitation diagrams, the easiest way is to introduce a parameter determined by the ratio of the critical buckling stress to the magnitude of the yield stress of the core material. In this case the limitation diagrams will not depend on the specific critical absolute values of stresses, but on their relationship; the nature of the diagrams will not depend on the density of the core. The design parameters of the core are determined on the basis of the construction of other diagrams for the given (required) values of generalized compressive stiffness, transverse shear, generalized critical compressive stresses and transverse shear of a unit cell of the sandwich structure which depend on the relative density of the truss core. The combination of these two constraint diagrams gives a more complete picture of the degree of optimality of the truss core design parameters.