Living cells exhibit, as most biological tissues, a stiffening (strain-hardening) response which reflects the nonlinearity of the stress-strain relationship. Tensegrity structures have been proposed as a comprehensive model of such a cell's mechanical response. Based on a theoretical model of a 30-element tensegrity structure, we propose a quantitative analysis of its nonlinear mechanical behavior under static conditions and large deformations. This study provides theoretical foundation to the passage from large-scale tensegrity models to microscale living cells, as well as the comparison between results obtained in biological specimens of different sizes. We found two non-dimensional parameters (L*-normalized element length and T*-normalized elastic tension) which govern the mechanical response of the structure for three types of loading tested (extension, compression and shear). The linear strain-hardening is uniquely observed for extension but differed for the two other types of loading tested. The stiffening response of the theoretical model was compared and discussed with the living cells stiffening response observed by different methods (shear flow experiments, micromanipulation and magnetocytometry).