This paper considers a modeling and analysis approach for the investigation of the linear and nonlinear steady-state dynamics of a base excited 3D tensegrity module carrying a top mass. The tensegrity module contains three compressive members, which may buckle and six cables (tendons). First, a dynamic model of the system is derived using Lagrange’s equation with constraints. The buckling modeling of the compressive members is based on the assumed-mode method with a single mode discretization. The tendons are modeled as piecewise linear springs, which can only take tensile forces. This research focusses on the dynamic stability of the tensegrity structure by defining the geometrical and material properties in such a way that the system is just below the static stability boundary. Static and linear dynamic analysis is performed. In the nonlinear steady-state analysis, frequency-amplitude plots, power spectral density plots, bifurcation point continuation diagrams, and Poincaré maps are presented. A tensegrity structure is designed and manufactured and an experimental set-up is realized in order to validate the model by comparing experimentally and numerically obtained responses. In the validation stage, the numerical results are based on an amplifier-shaker-tensegrity structure model. It can be concluded that the numerical results match partly quantitatively and partly qualitatively with the experimentally obtained responses.