The consideration of compliant tensegrity grids in the context of soft robotics is a promising area of research, offering the potential for systems with significant flexibility in both shape adaptation and change of mechanical properties. This study investigates two-dimensional (2D) tensegrity grids composed of compressed members that are indirectly linked via flexible, tensioned members. The focus of this paper is on the targeted and controlled realization of anisotropic properties of those tensegrity grids. Finally the findings are summarized and the application of tensegrity grids for the use in mobile robotics and soft grippers is outlined.