Modern civil engineering faces many problems that force engineers to seek for new, creative solutions, both within materials and structures. Due to the rapidly progressing urbanisation and the increasingly frequent requirement to strive for sustainable solutions, scientists have started to pay more attention to wood, which has been used in the construction for centuries. One of the first steps toward the improvement of this natural material was the development of wood-based products such as oriented strand board (OSB), laminated veneer lumber (LVL), glued or cross-laminated timber (GLT or CLT). These materials can be used in multi-storey buildings thanks to their improved load-bearing capacity and good elastic properties while maintaining a low weight. Example worth noting is a sandwich composite with wooden facings with a core made of a different species of wood, such as bamboo. The aim of the present project is to determine the feasibility of using a series of tensegrity modules in combination with a thin panel made of wood-based material. This is to make it possible to shape structural elements with smart characteristics, that is, with the ability to control their properties, for example, sandwich panels. In order to achieve this goal, analyses were carried out to check the effect of the ways in which tensegrity modules are connected to the slab on the behavior of the smart properties of the modules and, consequently, of the entire structure. The analyses were performed using the finite element method and the Abaqus program, as well as the author's codes. Funding: This research was funded in whole by the National Science Centre, Poland, grant number 2021/43/D/ST8/02238. For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.