In this research, a novel variable stiffness adaptive structure idea is explored based on a biologically-inspired actuation system concept recently developed by the authors. The new actuation system, inspired by the fibrillar network in plant cell walls, is synthesized using flexible matrix composites (FMCs). By tailoring the fibers (orientation, number of layers, material, etc.) and selection of matrix materials, one can achieve FMC structures that have an exceptionally high degree of anisotropy, making them attractive for many applications. In this research, fluid-filled FMC tubes are first utilized to examine the concept. By taking advantage of the fiber reinforcement configuration and the high bulk modulus of the pressurizing fluid in the FMC tubes, significant changes in stiffness can be achieved by varying the inlet valve to the tubes. Thus, the variable stiffness adaptive structure has the flexibility to easily deform when desired (open valve), possesses the high stiffness required during loading conditions when deformation is not desired (closed valve - locked state), and has the adaptability to vary the stiffness between the open/closed states through valve control. In this study, a closed-form, linear, structure/fluid analytical model for a single FMC tube is first developed, and parameter studies are performed for evaluating the axial stiffness variation of the tube between the open and closed valve states. The results demonstrate that significant variations in axial structural stiffness can be achieved through valve control. Based upon the findings of the single tube analysis, an analytical model of a multi-cellular beam structure with multiple FMC tubes is developed. The performance of such a structure under different loading conditions for both open- and closed valve scenarios is examined. Through valve control, the analytical findings demonstrate that the bending rigidity of the multi-cellular FMC structure can also be significantly varied.