The paper outlines several issues related to design of two-skin and multi-skin sandwich structures with a truss-reinforced polymeric core. The first part of the paper employs a simple analytical model that illustrates a contribution of such core to the facing stability. While the enhancement of the facing stability due to truss-reinforcement is shown to be considerable, the problems of local strength and truss element (pin) stability have to be analyzed prior to the acceptance of the design concept discussed in the paper. Accordingly, the second part of the paper presents the results of FEA used to pinpoint potentially weak elements in the considered design. The paper results in a number of practical conclusions and recommendations that may be useful for a development and implementation of sandwich structures with truss-reinforced polymeric cores.