As a relatively new class of load bearing elements, 3D-woven sandwich panels (3DWSPs) are emerging in many engineering applications. Similar to other structural elements, the practical usage of the 3DWSPs requires deep understanding around their mechanical properties like elastic stiffness and failure strength. The present study investigates the effect of load concentration on one-way response of the 3DWSPs by: (1) running a comprehensive set of 64 tests to find out the influence of various interfering parameters such as loading span length, the thickness of loaded skin, the shape of loading bar, and panel’s direction, (2) thoughtful interpretation of the elastic and failure results, (3) generation of failure maps, and (4) development of reliable theoretical models for the linear elastic response and the four observed failure mechanisms of skin indentation, skin wrinkling, core shear collapse, and interpillar skin buckling.