This paper outlines several issues related to the design of sandwich structures with a truss-reinforced polymeric or hollow core. The first part of the paper employs a simple analytical model that illustrates the contribution of such a core to the structure's 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 finite-element analysis 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 the development and implementation of sandwich structures with truss-reinforced cores.