The sandwich construction is an efficient lightweight design concept. It can be used to achieve structures with high flexural rigidity and – at the same time – with low weight. However, it should be noted that the resulting structures have a low transverse shear stiffness, which must not be neglected during the design. One way to improve their out-of-plane shear stiffness is the use of hybrid foam cores – meaning a foam core reinforced with composite struts. Based on a selected example, the potential of such hybrid core sandwich panels is to be examined numerically. The investigated configuration represents a sandwich panel with quasi-isotropic GFRP composite face layers and a foam core with unidirectionally reinforced GRP struts oriented at ±45 degrees to the panel normal. Aim of the present study is to numerically investigate the change in the out-of-plane and in-plane stiffness behavior of hybrid core sandwich panels compared to unstiffened foam cores, taking into account the weight increase. For this, finite element unit cell analyzes are performed using the homogenization software MEDTOOL [www.dr-pahr.at]. The results show that the in-plane and out-of-plane changes in the weight-related stiffness behavior are significantly different. On the one hand, depending on the chosen parameters, an up to 17% decrease in the specific in-plane engineering constants is observed compared to corresponding values of the unstiffened foam core sandwich. This decrease can be explained by the fact that the in-plane stiffness behavior is mainly influenced by the membrane behavior of the face layers and the GRP struts only cause an increase in weight. On the other hand, the results show that, depending on the chosen parameters, the weight-related values of the out-of-plane compressive stiffness can be increased up to 16-fold and the weight-related out-of-plane shear-stiffness values can even be increased up to 60-fold, in comparison to the corresponding results of an unstiffened foam core. Responsible for the significant increase in the out-of-plane shear-stiffness is the orientation of the GFRP-struts in the direction of the principal normal stresses. Since experimentally, the mechanical behavior of sandwich elements is usually examined with standardized tests, FE analyzes of standardized compression tests were carried out for comparison. Free-edge effects have been shown to have a significant impact on the out-of-plane normal stiffness values. Deviations of up to 23% are observed from the results of unit-cell studies mimicking the behavior of sandwich panels of infinite size. The reasons for this are the different Poisson's ratios between the face layers and the foam core and the fact that the struts cut off at the free edges no longer contribute to the out-of-plane normal stiffness. In order to make the experimental results of standardized compression tests usable for infinitely large hybrid core sandwich panels, a semi-analytical approach has been developed with which the influence of the free-edge effects can be estimated and the measurement results can be converted.