A novel non-linear analysis predicting behavior of extension-twist coupled flexible matrix composite tubes under multi-axial loadings is presented here. The composite device (called Sandwich Core Device) analyzed involves two concentric extension-twist coupled composite tubes with opposite angle of fibers. The annular space between the tubes is filled with an elastic-plastic foam core. Under tension, the tubes shear the foam material due to high intertube twist, resulting in energy absorption. The model combines large deformation theory of the laminated composite shells (using non-linear strain energy formulation) to the fracture mechanics and elastic-plastic deformation theory of the foam core. The model is capable of including material and geometric nonlinearities that arise from large deformation and fiber reorientation. It was found that for the cases considered, the model predictions exhibit close correlation with the experimental findings. Force versus strain response of the device is tailored with respect to variations in design parameters such as tube radius, resulting in wide ranges of loads and energy absorbing characteristics. The Sandwich Core Device exhibits specific energy absorption in excess of 3.5 J/g for the given core foam.